# Class 10

Explore popular questions from Coordinate Geometry for Class 10. This collection covers Coordinate Geometry previous year Class 10 questions hand picked by experienced teachers.

## Mathematics

Coordinate Geometry

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Q 1. The perimeter of the triangle whose vertices are {tex} ( - 1,4 ) ( - 4 , - 2 ) , ( 3 , - 4 ) {/tex} will be:

A

38

B

16

C

42

None of these

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Q 2. If {tex} \mathrm { P } ( 1,2 ) \mathrm { Q } ( 4,6 ) \mathrm { R } ( 5,7 ) {/tex} and {tex} \mathrm { S } ( \mathrm { a } , \mathrm { b } ) {/tex} are the vertices of a parallelogram {tex} \mathrm {PQRS}{/tex} than

A

{tex} a = 2 \quad b = 4 {/tex}

B

{tex} a = 3\ b = 4 {/tex}

{tex} a = 2\ b = 3 {/tex}

D

{tex} a = 3 \ b = 5 {/tex}

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Q 3. If {tex} ( 3 , - 4 ) {/tex} and {tex} ( - 6,5 ) {/tex} are the extremities of the diagonal of a parallelogram and {tex} ( - 2,1 ) {/tex} is its third vertex, then its fourth vertex is

{tex} ( - 1,0 ) {/tex}

B

{tex} ( 0 , - 1 ) {/tex}

C

{tex} ( - 1,1 ) {/tex}

D

None of these

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Q 4. The area of the triangle with vertices at the point {tex} ( a , b + c ) ( b , c + a ) , ( c , a + b ) {/tex} is

0

B

{tex} a + b + c {/tex}

C

{tex} a b + b c + c a {/tex}

D

None of these

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Q 5. A point {tex} \mathrm { A} {/tex} lies on {tex} \mathrm { x } {/tex} -axis and abscissa {tex} \mathrm { p } + \mathrm { q } {/tex}. Another point {tex} \mathrm { B } {/tex} lies on {tex} \mathrm { y } {/tex} -axis and has ordinate {tex} \mathrm { p } - \mathrm { q } {/tex}. Find the distance {tex} \mathrm { AB } {/tex} between them.

A

{tex} 2 \sqrt { \left( p ^ { 2 } + q ^ { 2 } \right) } {/tex} units

{tex} \sqrt { 2 \left( p ^ { 2 } + q ^ { 2 } \right) } {/tex} units

C

{tex} 2 \sqrt { \left( p ^ { 2 } - q ^ { 2 } \right) } {/tex}

D

None of these

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Q 6. The centroid, circumcentre, orthocentre in a triangle are:

A

always coincident

B

always collinear

C

always form a triangle

coincident in a equilateral triangle otherwise collinear

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Q 7. Area of quadrilateral formed by the lines {tex} | \mathrm { x } | + | \mathrm { y } | = 1 {/tex} is:

4

B

2

C

8

D

None of these

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Q 8. Match the following (one to one)
Column-I and column-II contains four entries each. Entries of column-I are to be matched with some entries of column-II. Only One entries of column-I may have the matching with the some entries of column- II and one entry of column-II Only one matching with entries of column-I Column II give the area of triangles whose vertices are given in column I match them correctly.

{tex} ( \mathrm { A } ) - ( \mathrm { S } ) {/tex}

B

{tex} ( \mathrm { B } ) - ( \mathrm { Q } ) {/tex}

C

{tex}(\mathrm C) - (\mathrm P ) {/tex}

D

{tex} (\mathrm D ) - (\mathrm R ) {/tex}

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Q 9. How many squares are possible if two of the vertices of a quadrilateral are {tex} ( 1,0 ) {/tex} and {tex} ( 2,0 ) ? {/tex}

A

1

B

2

3

D

4

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Q 10. The line {tex} 3 x + 4 y = 12 {/tex} cuts the axes at {tex} A {/tex} and {tex} B {/tex} if {tex} O {/tex} is the origin the area of {tex} \Delta O A B {/tex} is:

A

{tex} 12 \mathrm { sq } . {/tex} units

B

{tex} 9 \mathrm { sq. } {/tex} units

C

{tex} 24 \mathrm { sq } {/tex}. units

{tex} 6 \mathrm { sq. } {/tex} units

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Q 11. {tex} \mathrm { P } ( 3,1 ) \mathrm { Q } ( 6,5 ) {/tex} and {tex} \mathrm { R } ( \mathrm { x } , \mathrm { y } ) {/tex} are three points such that the angle {tex} \mathrm { PRQ } {/tex} is a right angle and the area of {tex} \Delta \mathrm { RQP } = 7 {/tex}. then the number of such points {tex} \mathrm { R } {/tex} is

A

0

B

1

2

D

4

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Q 12. The centroid of a triangle is {tex} ( 1,4 ) {/tex} and the coordinates of two of its vertices are {tex} ( 4 , - 3 ) {/tex} and {tex} ( - 9,7 ) . {/tex} The area of the triangle is:

A

183 sq. units

91.5 sq. units

C

124 sq. units

D

None of these

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Q 13. {tex} A ( 6,3 ) , B ( - 3,5 ) C ( 4 , - 2 ) {/tex} and {tex} D ( x , 3 x ) {/tex} are four points. If {tex} \Delta D B C: \Delta A B C = 1: 2 {/tex} then {tex} x {/tex} is equal to

{tex} 11 / 8 {/tex}

B

{tex} 8 / 11 {/tex}

C

{tex}3{/tex}

D

None

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Q 14. What will be the polar co-ordinates of the points {tex} ( 4,4 ) {/tex}

A

{tex} \left( 4 \sqrt { 2 } , 30 ^ { \circ } \right) {/tex}

{tex} \left( 4 \sqrt { 2 } , 45 ^ { \circ } \right) {/tex}

C

{tex} \left( 2 \sqrt { 2 } , 45 ^ { \circ } \right) {/tex}

D

{tex} \left( 2 \sqrt { 2 } , 30 ^ { \circ } \right) {/tex}

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Q 15. The line {tex} 2 x + 3 y = 6 {/tex} meets {tex} x {/tex} axis at the point:

{tex} ( 3,0 ) {/tex}

B

{tex} ( 0,3 ) {/tex}

C

{tex} ( 3,2 ) {/tex}

D

{tex} ( 2,3 ) {/tex}

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Q 16. Two mutually perpendicular straight lines through the origin from an isosceles triangles with the line {tex} 2 x + y = 5 . {/tex} Then the area of the triangle is

{tex} 5 {/tex}

B

{tex} 3 {/tex}

C

{tex} 5 / 2 {/tex}

D

{tex} 1 {/tex}

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Q 17. If the centroid of the triangle formed by the points {tex} ( a , b ) ( b , c ) {/tex} and {tex} ( c , a ) {/tex} is at the origin, then {tex} a ^ { 3 } + b ^ { 3 } + c ^ { 3 } {/tex}

A

{tex} { abc } {/tex}

B

0

C

{tex} a + b + c {/tex}

{tex} 3 { abc } {/tex}

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Q 18. The Co-ordinates of the fourth vertex of the parallelogram where of its vertices are {tex} ( - 3,4 ) ( 0 , - 4 ) {/tex} and {tex} ( 5,2 ) {/tex} can be

{tex} ( 8 , - 6 ) {/tex}

B

{tex} ( 2,0 ) {/tex}

C

{tex} ( - 8 , 2 ) {/tex}

D

None

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Q 19. A and B are two fixed points where Co-ordinate are {tex} ( 3,2 ) {/tex} and {tex} ( 5,4 ) {/tex} respectively. The Co-ordinate of a point P if ABP is an equilateral triangle

{tex} ( 4 - \sqrt { 3 } , 3 + \sqrt { 3 } ) {/tex}

B

{tex} ( 4 - \sqrt { 3 } , 3 - \sqrt { 3 } ) {/tex}

C

{tex} ( 3 - \sqrt { 3 } , 4 + \sqrt { 3 } ) {/tex}

D

{tex} ( 3 + \sqrt { 3 } , 4 - \sqrt { 3 } ) {/tex}

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Q 20. If three given points {tex} \mathrm { A } , \mathrm { B } , \mathrm { C } {/tex} are collinear, then

A

area of {tex} \triangle \mathrm { ABC } {/tex} is 0

B

slope of {tex} \mathrm { AB } = {/tex} slope of {tex} \mathrm { BC } = {/tex} slope of {tex} \mathrm { AC } {/tex}

C

distance between {tex} \mathrm A {/tex} and {tex}\mathrm B = {/tex} distance between {tex}\mathrm B {/tex} and {tex}\mathrm C = {/tex} distance between {tex}\mathrm A {/tex} and {tex}\mathrm C {/tex}

All of the above

##### Explanation

If three points are collinear: 1. Area of triangle method(i.e. 0). 2. Slope formula method to find that points are collinear. 3. Three or more points are collinear, if slope of any two pairs of points is same. 4. With three points A, B and C, three pairs of points can be formed, they are: AB, BC and AC. 5. If Slope of AB = slope of BC = slope of AC, then A, B and C are collinear points.

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Q 21. When four points are given

A

They form a square if all sides are equal and diagonals are also equal

B

They form a rectangle if the opposite sides are equal and diagonals are also equal

C

They form a rhombus if all sides are equal but diagonals are not equal

All of the above

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Q 22. If polar co-ordinate of any points are {tex} ( 2 , \pi / 3 ) {/tex} then its cartesian co-ordinates will be:

{tex} ( 1 , \sqrt { 3 } ) {/tex}

B

{tex} ( - 1 , \sqrt { 3 } ) {/tex}

C

{tex} ( - 1 , - \sqrt { 3 } ) {/tex}

D

{tex} ( 1 , - \sqrt { 3 } ) {/tex}

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Q 23. Two lines {tex} a _ { 1 } x + b _ { 1 } y + c _ { 1 } = 0 {/tex} and {tex} a _ { 2 } x + b _ { 2 } y + c _ { 2 } = 0 {/tex} are:

A

parallel if {tex} \frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } \neq \frac { c _ { 1 } } { c _ { 2 } } {/tex}

B

perpendicular if {tex} a _ { 1 } a _ { 2 } + b _ { 1 } b _ { 2 } = 0 {/tex}

C

intersecting if {tex} \frac { a _ { 1 } } { a _ { 2 } } \neq \frac { b _ { 1 } } { b _ { 2 } } {/tex},coincident if {tex} \frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } = \frac { c _ { 1 } } { c _ { 2 } } {/tex}

All of the above

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Q 24. The distance between the points {tex} A ( 0,6 ) {/tex} and {tex} B {/tex} {tex} ( 0 , - 2 ) {/tex} is :

A

6

8

C

4

D

2

##### Explanation

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Q 25. The distance between the points {tex} ( 0,5 ) {/tex} and {tex} ( - 5,0 ) {/tex} is :

A

{tex}5{/tex}

{tex} 5 \sqrt { 2 } {/tex}

C

{tex} 2 \sqrt { 5 } {/tex}

D

{tex}10{/tex}