Coordinate Geometry — Chapter Test | Class 9 IMO

Q1

Starting from the origin, a point moves 3 right, 2 up, 3 left, then 2 down. Where does it end?

(0,0) → (3,0) → (3,2) → (0,2) → (0,0): it returns to the origin.

Q2

For M(4, −3) and N(−2, 7), the value of (ordinate of N) − (ordinate of M) is:

7 − (−3) = 7 + 3 = 10.

Q3

On plotting O(0, 0), A(3, 0), B(3, 4), C(0, 4) and joining OA, AB, BC, CO, which figure is obtained?

Adjacent sides are perpendicular with lengths 3 and 4 (unequal), so the figure is a rectangle.

Q4

Three vertices of a square are (−1, 2), (3, 2) and (3, −2). The fourth vertex is:

Sides have length 4; the fourth vertex aligns with x = −1 and y = −2, giving (−1, −2).

Q5

Four friends stand at A(2, 2), B(−2, 2), C(−2, −2), D(2, −2). The perimeter of the square they form is:

Each side is 4 units, so the perimeter is 4 × 4 = 16 units.

Q6

Find the distance between C(−1, −2) and D(2, 2).

Horizontal change 3 and vertical change 4 give distance √(3² + 4²) = √25 = 5 units.

Q7

Assertion (A): The point (0, 3) lies on the y-axis. Reason (R): The x-coordinate of any point on the y-axis is zero. Which is correct?

(0, 3) has x = 0 so it lies on the y-axis, and R correctly explains this.

Q8

The distance of the point P(−6, 8) from the origin is:

By Pythagoras, distance = √(6² + 8²) = √(36 + 64) = √100 = 10 units.

Q9

A driver starts at O(0, 0), drives 5 km along the positive x-axis to A, then 12 km parallel to the positive y-axis to B. The straight-line distance OB is:

OB = √(5² + 12²) = √(25 + 144) = √169 = 13 km.

Q10

If (a, b) lies in Quadrant II, then (−a, −b) lies in:

In Quadrant II, a < 0 and b > 0, so −a > 0 and −b < 0, which is Quadrant IV.

Q11

Find the area of the triangle formed by O(0, 0), A(6, 0) and B(0, 5).

Right-angled at O with base 6 and height 5: area = ½ × 6 × 5 = 15 sq units.

Q12

Three corners of a rectangular plot are (1, 1), (7, 1) and (1, 5). The fourth corner is:

The fourth corner aligns with x = 7 and y = 5, giving (7, 5).

Q13

Find the perpendicular distance of the point P(5, 7) from the y-axis.

The distance of a point from the y-axis equals the absolute value of its x-coordinate, which is 5.

Q14

A circle is centred at the origin and passes through (6, 8). Which of these points lies OUTSIDE the circle?

Radius² = 6² + 8² = 100. (0,10): 100 (on), (3,4): 25 (inside), (−8,6): 100 (on), (7,8): 49 + 64 = 113 > 100 (outside).

Q15

A point has equal non-zero numerical values for its abscissa and ordinate (|x| = |y|). On which line can it NOT lie?

|x| = |y| means y = x or y = −x (i.e. x + y = 0). The line x + y = 5 need not satisfy |x| = |y|.