Genius Jnr - Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, −3). Also, find the value of x. [CBSE 2014]

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Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, −3). Also, find the value of x. [CBSE 2014]

manures provide humus to the soil whereas fertilizers do not provide humus to the soil

manures are rich in inorganic matter while fertilizers are not rich in inorganic matter

manures can be stored for a long time whereas fertilizers cannot be stored for long time

manures are prepared in factories while fertilizers are prepared in the fields

or

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1 2 B 4 3 C 6 6 Three Vertices Parallelogram Abcd Find Coordinates Fourth Vertex P 2 P Mid Point Line Segment Joining Points 6 5 B 2 11 Find Value P P X 6 Mid Point Line Segment Joining 6 5 B 4 Find Distance Points 3 0 0 5 Units Positive Value P 2 6 Mid Point Line Segment Joining 6 5 B 4 Find Distance Points C 0 B 0 C Find Value Point 3 Lies Line Represented 2x 3y 5 0 Find Distance Points 85 2 25 2 Write Ratio Line Segment Doining Points 3 6 B 5 3 Divided X Axis Find Values X Distance Point P 2 3 Q X 5 10 Write Condition Collinearity Points X1 Y1 X2 Y2 X3 Y3 Write Formula Area Triangle Vertices X1 Y1 X2 Y2 X3 Y3 Points Q Reflections Point P 3 4 X Axes Respectively Qr Write Coordinates Reflections Points 3 5 X Axes Two Vertices Triangle Coordinates 8 7 9 4 Centroid Triangle Origin Coordinates Third Vertex Mid Point Segment Joining X 1 B X 1 2 C 32 52 Find X Write Coordinates Point X Axis Equidistant Points 3 4 2 5 Following Solutions Conduct Electricity Centroid Triangle Formed Points P B Q B C R C Origin Value B C Write Coordinates Point Dividing Line Segment Joining Points 2 3 3 4 Internally Ratio 1 5 Area Triangle Formed Points 0 0 6 0 B 0 4 Distance Points X 0 0 3 5 Values X Following Salts Minimum Ph Value Distance Points 5 Sin 60 0 0 5 Sin 30 Write Ratio Line Segment Joining Points 2 3 3 2 Divided X Axis Write Perimeter Triangle Formed Points 0 0 0 B 0 B Write Distance Points 10 Cos 0 B 0 10 Sin Line Segment Joining Points 3 4 1 2 Trisected Points P 2 Q 53 B 83 B 23 B 73 B 0 C 13 B 1 23 B 13 Ratio Line Segment Joining Points A1 B1 B A2 B2 Divided Axis A1 A2 B A1 A2 C B1 B2 B1 B2 Ratio Line Segment Joining P X1 Y1 Q X2 Y2 Divided X Axis Y1 Y2 B Y1 Y2 C X1 X2 X1 X2 Length Line Segment Joining 2 3 B 10 Units Abscissa B 10 Units Ordinates 3 9 B 3 9 C 6 27 6 27 Coordinates Fourth Vertex Rectangle Formed Points 0 0 2 0 0 3 3 0 B 0 2 C 2 3 3 2 2 1 Centroid Triangle Vertices X 0 5 2 8 X Satisfy Relation 3x 8y 0 B 3x 8y 0 C 8x 3y 0 8x 3y Centroid Triangle Formed Points 3 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Axis Ratio 1 3 B 2 3 C 3 1 2 3 Centroid Triangle 1 4 Two Vertices 4 3 9 7 Area Triangle 183 Sq Units B 1832 Sq Units C 366 Sq Units Points 0 0 B 1 1 Collinear 1a 1b 1 B 2 C 0 1 Area Triangle Formed Points X 2x 2 6 3 1 5 Square Units X 23 B 35 C 3 5 Points 2t 2 6 3 1 Collinear 34 B 43 C 53 35 X 2 3 4 7 5 Collinear X 60 B 63 C 63 60 Area Triangle Formed B C B C C B B C B Abc C B C 2 0 5 3 B 11 5 P 12 Vertices Right Triangle Right Angled P 2 4 B 2 4 C 2 4 2 4 1 2 2 1 3 1 Three Vertices Parallelogram 2 B 0 B 2 B 0 C 2 B 6 6 B 2 Coordinates Point X Axis Equidistant Points 3 4 2 5 20 0 B 23 0 C 45 0 None Following Compounds Burns Sooty Flame Three Points 0 0 3 3 3 Form Equilateral Triangle 2 B 3 C 4 None 2 2 B 4 4 C 5 8 Vertices Triangle Length Median Vertex C 65 B 117 C 85 113 Perimeter Triangle Formed Points 0 0 0 1 0 1 1 2 B 2 1 C 3 2 2 Propanoic Acid Carbon Compound Whose Functional Group Represented Use Following Information Answer Next Question Dehydration Ethanol Leads Formation Ofas Major Produc Distance Points Cos B Sin 0 0 Sin B Cos A2 B2 B B C A2 B2 A2 B2 X Positive Integer Distance Points P X 2 Q 3 6 10 Units X 3 B 3 C 9 9 Distance Points Cos 25 0 0 Cos 65 B 2a C 3a None Mark Correct Alternative Following Distance Points Cos 0 Sin Cos 3 B 2 C 2 1 Find Value Area Triangle Formed Points 2a B 2 6 C 3 1 10 Square Units Find Value K Points 8 1 B 3 4 C 2 K Collinear R X Point Line Segment Joining Points P B Q B Prove X B Point P 3 Lies Line Segment Joining Points 25 6 B 2 8 Find Value Find Value K Points 7 2 B 5 1 C 3 2k Collinear Find Value K Points K 3 B 6 2 C 3 4 Collinear X Line Joining Two Points 1 3 4 2 Prove X 2 0 Three Points X1 Y1 X2 Y2 X3 Y3 Lie Line Prove Y2 Y3x2x3 Y3 Y1x3x1 Y1 Y2x1x2 0 Prove Points B A1 B1 A1 B B1 Collinear Ab1 A1b Hardness Water Attributed Presence Four Points 6 3 B 3 5 C 4 2 X 3x Given Way Dbc Abc 12 Find X Dobereiner Triads Three Elements Arranged Downwards Order Area Triangle 5 Two Vertices 2 1 3 2 Third Vertex Lies X 3 Find Third Vertex Newlands Arranged Known Elements Order Prove Points 0 0 B 1 1 Collinear 1a 1b 1 Mendeleev Periodic Law States Properties Elements Periodic Function Vertices Abc 2 1 5 4 2 3 Respectively Find Area Triangle Length Altitude Use Following Information Answer Next Question Periods Groups Mendeleev Periodic Table Information A Eka Boron Eka Aluminium Alternative Numbers Periods Groups Modern Periodic Table Correctly Listed Find Third Vertex Triangle Two Vertices 3 1 0 2 Centroid Origin Fig 14 36 Right Triangle Boa Given C Mid Point Hypotenuse Ab Show Equidistant Vertices B 2 3 4 3 4 5 Mid Points Sides Triangle Find Coordinates Centroid G Centroid Triangle Abc Prove Ab2 Bc2 Ca2 3 Ga2 Gb2 Gc2 G Centroid Triangle Abc P Point Plane Prove Pa2 Pb2 Pc2 Ga2 Gb2 Gc2 3gp2 Prove Lines Joining Middle Points Opposite Sides Quadrilateral Join Middle Points Diagonals Meet Poi Prove Analytically Line Segment Joining Middle Points Two Sides Triangle Equal Half Third Side Two Vertices Triangle 1 2 3 5 Centroid Origin Find Coordinates Third Vertex Find Centroid Triangle Whose Vertices 1 4 1 1 3 2 Ii 2 3 2 1 4 0 Find Coordinates Point Ab Diameter Circle Whose Centre 2 3 B 1 4 Ratio Point 4 6 Divide Line Segment Joining Points 6 10 B 3 8 Points 6 1 B 8 2 C 9 4 K P Vertices Parallelogram Taken Order Find Values K P Find Ratio Axis Divides Line Segment Joining Points 5 6 1 4 Also Find Coordinates Point Division Show 3 2 B 5 5 C 2 3 4 4 Vertices Rhombus Abcd Rectangle Formed Joining Points 1 1 B 1 4 C 5 4 5 1 P Q R Mid Points Sides Ab Bc Cd Da Respecti 4 2 B 6 5 C 1 4 Vertices Abc Median Meets Bc Find Coordinates Point Ii Find Coordinates Point P Ad A Find Coordinates Points Divide Line Segment Joining 2 2 B 2 8 Four Equal Parts B Two Points Coordinates 2 2 2 4 Respectively Find Coordinates P Ap 37ab Line Joining Points 2 1 5 8 Trisected Points P Q Point P Lies Line 2x K 0 Find Value K Determine Ratio Point 6 Divides Join 3 1 B 8 9 Also Find Value Determine Ratio Point P 6 Divides Join 4 3 B 2 8 Also Find Value Show Points 1 0 B 5 3 C 2 7 2 4 Vertices Parallelogram B 1 4 5 2 Respectively Find Coordinates P Ap Bp 3 4 Find Distance Point 1 2 Mid Point Line Segment Joining Points 6 8 2 4 Show Mid Point Line Segment Joining Points 5 7 3 9 Also Mid Point Line Segment Joining Points 8 6 0 Find Coordinates Points Divide Line Segment Joining Points 4 0 0 6 Four Equal Parts Find Length Medians Abc Vertices 0 1 B 2 1 C 0 3 Coordinates Mid Points Sides Triangle 3 2 3 1 4 3 Find Coordinates Vertices Three Consecutive Vertices Parallelogram 1 2 3 6 5 10 Find Fourth Vertex Points 2 0 B 9 1 C 11 6 4 4 Vertices Quadrilateral Abcd Determine Whether Abcd Rhombus Points 2 1 1 0 X 3 1 Form Parallelogram Find Values X Line Segment Joining Points P 3 3 Q 6 6 Trisected Points B Nearer P Also Lies Line Given 2x K 0 Find Coordinates Mid Points Sides Triangle 3 4 4 6 5 7 Find Vertices Two Vertices Parallelogram 3 2 1 0 Diagonals Cut 2 5 Find Vertices Parallelogram Three Vertices Parallelogram B B 2a B 2a B B B Find Fourth Vertex Find Lengths Medians Triangle Whose Vertices 1 3 B 1 1 C 5 1 Prove Points 4 1 2 4 4 0 2 3 Vertices Rectangle Prove 4 3 6 4 5 6 3 5 Angular Points Square Prove Points 4 5 7 6 6 3 3 2 Vertices Parallelogram Rectangle Find Ratio Line Segment Joining 2 3 5 6 Divided X Axis Ii Axis Also Find Coordinates Point Division Determine Ratio Straight Line X 2 0 Divides Line Segment Joining 3 1 8 9 Mid Point Line Joining 3 4 K 7 X 2x 2y 1 0 Find Value K Ratio Line Segment Joining Points 2 3 3 7 Divided Axis Also Find Coordinates Point Division Ii Rati Vertex Triangle 1 1 Middle Points Sides 2 3 5 2 Find Vertices Coordinates Mid Points Sides Triangle 1 1 2 3 3 4 Find Vertices Triangle 1 3 B 1 1 C 5 1 Vertices Triangle Abc Find Length Median Find Ratio Point 2 Divides Line Segment Joining Points 2 2 B 3 7 Also Find Value Points 3 4 6 2 Extremities Diagonal Parallelogram Third Vertex 1 3 Find Coordinates Fourth Vertex Three Consecutive Vertices Parallelogram 2 1 1 0 4 3 Find Fourth Vertex Prove Points 3 2 4 0 6 3 5 5 Vertices Parallelogram Find Coordinates Point Diagonals Parallelogram Formed Joining Points 2 1 1 0 4 3 1 2 Meet Find Points Trisection Line Segment Joining Points 5 6 7 5 B 3 2 3 4 C 2 2 7 4 Find Coordinates Point Divides Line Segment Joining 1 3 4 7 Internally Ratio 3 4 Find Relation X Point X Equidistant Points 3 6 3 4 Find Point Axis Equidistant Form Points 5 2 3 2 Seating Arrangement Desks Classroom Three Students Rohini Sandhya Bina Seated 3 1 B 6 4 C 8 6 Think Prove Points 3 0 4 5 1 4 2 1 Taken Order Form Rhombus Also Find Area Find Equation Perpendicular Bisector Line Segment Joining Points 7 1 3 5 Name Quadrilateral Formed Following Points Given Reasons Answers 1 2 B 1 0 C 1 2 3 0 Ii 3 5 B 3 1 C Two Opposite Vertices Square 1 2 3 2 Find Coordinates Two Vertices Find Centre Circle Passing 6 6 3 7 3 3 Find Values Distance Points P 2 3 Q 10 10 Units Q 0 1 Equidistant P 5 3 R X 6 Find Values X Also Find Distances Qr Pr Point P X Equidistant Points 5 1 B 1 5 Prove X Prove Points 0 0 5 5 5 5 Vertices Right Isosceles Triangle Find Value X Pq Qr Coordinates P Q R 6 1 1 3 X 8 Respectively Find Point X Axis Equidistant Points 2 5 2 3 Show Points 5 6 B 1 5 C 2 1 6 2 Vertices Square Ii Prove Hat Points 2 3 B 2 2 C 1 2 3 1 Vertices Sq Find Point X Axis Equidistant Points 7 6 3 4 Find Coordinates Circumcentre Triangle Whose Vertices 3 0 1 6 4 1 Also Find Circumradius Show Points 3 2 5 5 2 3 4 4 Vertices Rhombus Find Area Rhombus Two Opposite Vertices Square 5 4 1 6 Find Coordinates Remaining Two Vertices Find Value K Point P 0 2 Equidistant 3 K K 5 Find Centre Circle Passing 5 8 2 9 2 1 Find Angle Subtended Origin Line Segment Whose End Points 0 100 10 0 Find Circumcentre Triangle Whose Vertices 2 3 1 0 7 6 Three Vertices Parallelogram 3 4 3 8 9 8 Find Fourth Vertex Point Axis Equidistant 2 3 4 1 Coordinates Point P 3 2 Find Coordinates Point Q Lies Line Joining P Origin Op Oq Prove Points 2 5 0 1 2 3 Collinear Point X Axis Equidistant 5 9 4 6 Two Vertices Isosceles Triangle 2 0 2 5 Find Third Vertex Length Equal Sides 3 Show Quadrilateral Whose Vertices 2 1 3 4 2 3 3 2 Rhombus Equilateral Triangle Two Vertices Points 3 4 2 3 Find Coordinates Third Vertex Prove Points 2 3 4 6 1 3 2 Form Triangle Prove Points 2a 4a 2a 6a 2a 3a 5a Vertices Equilateral Triangle Prove 2 2 2 1 5 2 Vertices Right Angled Triangle Find Area Triangle Length Hypotenuse Prove Points 3 0 6 4 1 3 Vertices Right Angled Isosceles Triangle Prove Points 1 7 B 4 2 C 1 1 4 4 Vertices Square Show Points 1 2 B 3 6 C 5 10 3 2 Vertices Parallelogram Show Points 4 1 2 4 4 0 2 3 Vertices Points Rectangle Length Line Segment 10 Units Coordinates One End Point 2 3 Abscissa End 10 Find Ordinate End Find Values X Distances Point X 3 0 Well 3 0 4 Points 2 1 1 2 Equidistant Point X Show X 3y 0 Find Value Distance Points 3 4 1 10 Find Distance Following Pair Points 6 7 1 5 B B B C B C B C Asin Bcos Acos Bsin 0 0 B Base Pq Two Equilateral Triangles Pqr Pqr Side 2a Lies Along Axis Mid Point Pq Origin Find Coordinat Let Abcd Square Side 2a Find Coordinates Vertices Square Coincides Origin Ab Ad Along Ox Oy Respecti Axis Following Points Lie P 5 0 B Q 0 2 C R 4 0 0 5 Point 0 2 Equidistant Points B 3 P C P 5 Find Value P Cbse 2012 2013 Prove Points 7 10 2 5 3 4 Vertices Isosceles Right Triangle Cbse 2013 Point P Divides Line Segment Joining Points 3 5 B 4 8 Appb K1 P Lies Line X 0 Find Value K Cbse 2012 Find Ratio Point P 1 Lying Line Segment Joining 3 10 B 6 8 Divides Also Find Value Cbse 2013 Find Area Parallelogram Abcd Three Vertices 2 4 B 2 3 5 C 2 6 Cbse 2013 Coordinates One End Diameter Circle 2 3 Coordinates Centre 2 5 Coordinates End Diameter 6 7 B 6 7 C Coordinates Point P Dividing Line Segment Joining Points 1 3 B 4 6 Ratio 2 1 2 4 B 3 5 C 4 2 5 3 Cbs Fig 14 46 Area Abc Square Units 15 B 10 C 7 5 2 5 Cbse 2013 Point X Axis Equidistant Points 1 0 5 0 0 2 B 2 0 C 3 0 0 3 Cbse 2013 Following Statements Fertilizers Correct Point P 2 2 Equidistant Points 2 K B 2k 3 Find K Also Find Length Ap Cbse 2014 Point 0 2 Equidistant Points B 3 P C P 5 Find P Also Find Length Ab Cbse 2014 3 Equidistant Points P 8 3 Q 7 6 Find Value Find Distance Aq Cbse 2014 Point P K 1 2 Equidistant Points 3 K B K 5 Find Values K Cbse 2014 0 3 0 3 Two Vertices Equilateral Triangle Find Coordinates Third Vertex Cbse 2014 Points P Q R Divides Line Segment Joining 1 2 B 6 7 5 Equal Parts Find Coordinates Points P Q R Cbse Mid Point P Line Segment Joining Points 10 4 B 2 0 Lies Line Segment Joining Points C 9 4 4 Find Rat Find Ratio Point P34 512 Divides Line Segment Joining Points A12 32 B2 5 Cbse 2015 Find Ratio Line Segment Joining Points 3 3 B 2 7 Divided X Axis Also Find Coordinates Point Division Find Ratio Point P X 2 Divides Line Segment Joining Points 12 5 B 4 3 Also Find Value X Cbse 2014 Following Systems Irrigation Modern Method Irrigation Find Value K Points 3k 1 K 2 K K 7 K 1 K 2 Collinear Cbse 2014 Use Following Information Answer Next Question Systems Part Traditional Methods Irrigation Informati Points 2 1 B B C 4 1 Ae Collinear B 1 Find Values B Cbse 2014 Weedicides Chemicals Used Controlling Weeds Present Fields Stage Development Weeds Weedicides Spraye P 5 3 Q 4 6 R 2 3 1 2 Vertices Quadrilateral Pqrs Find Area Cbse 2015 Find Area Triangle Pqr Q 3 2 Mid Points Sides Q 2 1 1 2 Cbse 2015 4 9 B 2 3 C 6 5 Vertices Abc Length Median C 5 Units B 10 Units C 25 Units 10 Units Cbse 2014 Distance Points Asin Cos 0 B0 Sin Cos Cbse 2015 P 2 4 Q 0 3 R 3 6 5 Vertices Parallelogram Pqrs Value 7 B 5 C 7 8 Cbse 2014 X 2 B 3 4 C 7 5 Collinear Value X 63 B 63 C 60 B 60 Cbse 2014 Perimeter Triangle Vertices 0 4 0 0 3 0 7 5 B 5 C 10 12 Cbse 2014 Find Point Equidistant Points 5 4 B 1 6 Many Points Centre Circle 2a 7 Find Values Circle Passes Point 11 9 Diameter 102 Units Ayush Starts Walking House Office Instead Going Office Directly Goes Bank First Daughter School Reac 4 3 4 3 Two Vertices Equilateral Triangle Find Coordinates Third Vertex Given Origin Lies Interior I P 9a 2 B Divides Line Segment Joining 3a 1 3 B 8a 5 Ratio 3 1 Find Values B B Mid Point Line Segment Joining Points 10 6 B K 4 2b 18 Find Value K Distance Ab Point C 1 2 Divides Internally Line Segment Joining Points 2 5 B X Ratio 3 4 Find Value X2 Y2 Abcd Parallelogram Vertices X1 Y1 B X2 Y2 C X3 Y3 Find Coordinates Fourth Vertex Terms X1 X2 X3 Y1 Y Points X1 Y1 Bx2 Y2 Cx3 Y3 Vertices Abc Median Meets Bc Find Coordinates Point Ii Find Coordinates P Q Abc Coordinates Vertex 0 1 1 0 E 0 10 Respectively Mid Points Sides Ab Ac F Mid Points Side Bc Find Points 1 2 B 2 3 C 2 4 3 Form Parallelogram Find Value Height Parallelogram Taking Ab Base A6 1 B 8 2 C 9 4 Three Vertices Parallelogram Abcd E Mid Point Dc Find Area Ade 15 52 E 7 3 F72 72 Mid Points Sides Abc Find Area Abc Q Find Area Triangle Vertices B C B C C B Points 1 2 0 0 C B Collinear Find B Point P 2 1 Lies Line Segment Joining Points 4 20 B 8 4 Ap 13ab B Ap Bp C Pb 13ab Ap 12ab Line Intersects Axis X Axis P Q Respectively 2 5 Mid Point Pq Coordinates P Q Respectively 0 5 2 0 B Find Coordinates Point Equidistant Three Vertices 2x 0 0 0 B 0 2y Aob Show Abc 2 0 B 2 0 C 0 2 Pqr P 4 0 Q 4 0 R 0 2 Similar Triangles B 0 Prove Points A2 B B2 0 0 Collinear Area Triangle 5 Sq Units Two Vertices 2 1 3 2 Third Vertex 72 Find Value Distance Points 4 K 1 0 5 Possible Values K Points 2 9 B 5 C 5 5 Vertices Triangle Abc Right Angled B Find Values Hence Area Abc Find Ratio P 4 Divides Line Segment Joining Points 2 3 B 6 3 Hence Find Find Distance Point P X Origin Points 11 B 5 B C 2 15 1 1 Vertices Parallelogram Abcd Find Values B Ii Point 3 1 B 5 1 C B 4 3 Ver Points P Q Trisect Line Segment Joining Points 2 0 B 0 8 P Near Find Coordinates P Q Ii Line Segmen Find Area Triangle Whose Vertices 6 3 3 5 4 2 Ii At12 2at1 At22 2at2 At32 2at3 Iii C C C Iv 1 1 4 6 Vertices Triangle 1 3 4 P 9 7 Area 15 Sq Units Find Value P Ii Find Value K Area Triangle Abc K 1 1 Find Value X Distance Points 0 0 B X 4 5 Units Write Coordinates Point P X Axis Equidistant Point 2 0 B 6 0 Distance Point 2 3 X Axis Distance Point 4 7 Axis Image Point 3 5 X Axis Coordinates Coordinates Image Point 4 5 Axis Distance Points 0 5 5 0 Distance Points 2 2 1 X 5 Values X Area Triangle Vertices 3 0 B 7 0 C 8 4 Quadrant Point Dividing Line Segment Joining Points 7 6 3 4 Internally Ratio 1 2 X Coordinate Point Lying Perpendicular Bisector Line Segment Joining Points 2 5 B 2 5 P 3 4 Mid Point Line Segment Joining Points Q 6 5 R 2 3 Value Coordinates Point Equidistant Vertices Triangle Formed Points 0 0 0 B 0 B Points 0 0 B 1 1 Collinear 1a 1b Distance Point 4 X Axis Half Distance Axis Distance Points 3 14 B 5 9 Units Points 5 1 2 3 8 2m Collinear Ratio Point P34 512 Divides Line Segment Joining Points 1 2 3 2 B 2 5 X Axis Divides Line Segment Joining Points 4 6 1 7 Ratio Values Point 2 4 Equidistant Points 3 8 10 Distance Points 4 P 1 0 5 Values P Coordinates Point Equidistant Vertices 0 0 6 0 B 0 8 Oab Number Points X Axis Distance 25 Point 7 4 Distance Points 1 0 2 Cot Centroid Triangle Whose Vertices 2 4 3 4 2 3 2 2 5 2 Opposite Vertices Square Length Side Square Centroid Triangle Formed Points B 1 B 1 Origin A3 B3 1ab