CBSE Board Test Paper Chapter_Coordinate Geometry

CBSE TEST PAPER UNIT: 4 (coordinate geometry)

The method of describing the location of points in this way was proposed by the French mathematician René Descartes (1596 - 1650). (Pronounced "day CART"). He proposed further that curves and lines could be described by equations using this technique, thus being the first to link algebra and geometry. In honor of his work, the coordinates of a point are often referred to as its Cartesian coordinates, and the coordinate plane as the Cartesian Coordinate Plane.

A system of geometry where the position of points on the plane is described using an ordered pair of numbers.

In coordinate geometry, points are placed on the "coordinate plane" as shown below. It has two scales - one running across the plane called the "x axis" and another a right angles to it called the y axis. (These can be thought of as similar to the column and row in the paragraph above.) The point where the axes cross is called the origin and is where both x and y are zero.

                                                                 
                                                                         











                                                        Section-A

Choose the correct answer from the given four options:

1. The distance of the point P (2, 3) from the x-axis is

(A) 2                            (B) 3                (C) 1                           (D) 5

2. The distance between the points A (0, 6) and B (0, –2) is

(A) 6                            (B) 8                (C) 4                           (D) 2

3. The distance of the point P (–6, 8) from the origin is

(A) 8                            (B) 2 √7          (C) 10                          (D) 6

4. The distance between the points (0, 5) and (–5, 0) is

(A) 5                            (B) 5√ 2          (C) 2 √5                      (D) 10

5. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is

(A) 5                            (B) 3                (C) √ 34                    (D) 4

Section-B

1. Find the coordinates of the mid point of the line segment joining the points (4, 3) and (2, 1).

2. Find the coordinates of the point which divides the line segment joining the points (1, 3) and (2, 7) in the 

ratio 3: 4.

3. Show that the points (1, 1), (3, - 2) and (- 1, 4) are collinear.

4. Find the centroid of the triangle whose vertices are (3, - 5); (- 7, 4) and (10, - 2).

5. If the distance of the point P(x, y) from the points A (5, 1) and B (- 1, 5) is equal, show that 3x = 2y.

6. Find the area of a triangle whose vertices are A (1, 2); B (3, 5) and C (- 4, - 7)

7. In what ratio does the point P (- 4, 6) divide the line segment joining the points A (- 6, 10) and B (3, - 8).

8. For what value of m, the points (4, 3), (m, 1) and (1, 9) are collinear.

9. Prove that the coordinates of the centroid of a triangle ABC with vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are given by  [(x₁+x₂+x₃)/3] , [ )y₁+y₂+y₃)/3]

10. Prove that the diagonals of a rectangle bisect each other and are of equal length 

11. Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ: QE = 2: 1 and CR: RF = 2: 1.

12. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1, 3) and (2, 7).

13. PQRS is a square of side .b. units. If P lies at the origin, sides PQ and PS lie along x - axis and y - axis  respectively, find the coordinates of the vertices of the square PQRS.

14. If the points (5, 4) and (x, y) are equidistant from the point (4, 5); then show that   x² + y² - 8x -10y + 39 = 0

15. The line segment joining the points (3, - 4) and (1, 2) is trisected at the points P and Q. If he coordinates of P and Q are (p, -2) and (5/3, q) respectively, Find the value of p and q. 

10th Maths SA-2 Chapter Links

Quadratic Equations

Arithmetic Progressions

Height and Distance

Co-ordinate Geometry

Circles

Area Related to Circles

Surface Areas and Volumes

Probability