Class 10 Maths Chapter 7 Question Answers - Coordinate Geometry

Coordinate Geometry

Q1. Find a point on the y-axis equidistant from (− 5, 2) and (9, − 2).

Let the required point on the y-axis be P (0, y)

∴ PA = PB

⇒ y² − y² − 4y − 4y = 81 + 4 − 4 − 25
⇒ − 8y = 85 − 29
⇒ − 8y = 56

⇒  

∴ The required point is (0, −7).

Q2. Find a point on x-axis at a distance of 4 units from point A (2, 1).

Let the required point on x-axis be P (x, 0).

∴ PA = 4

⇒ x² − 4x + 4 + 1 = 4² = 16
⇒ x² − 4x + 1 + 4 − 16 = 0
⇒ x² − 4x − 11 = 0

⇒  

Q3. Find the distance of the point (3, − 4) from the origin.

The coordinates of origin (0, 0).
∴ Distance of (3, − 4) from the origin

Q4. For what value of x is the distance between the points A (− 3, 2) and B (x, 10) 10 units?

The distance between A (− 3, 2) and B (x, 10)

⇒ (x + 3)² + (8)² = 10²
⇒ (x + 3)² = 10² − 8²
⇒ (x + 3)² = (10 − 8) (10 + 8) = 36
⇒  
For +ve sign, x =6 − 3 = 3
For −ve sign, x = − 6 − 3 = − 9

Q5. Find a point on the x-axis which is equidistant from points A (5, 2) and B (1, − 2).

The given points are: A (5, 2) and B (1, − 2) Let the required point on the x-axis be C (x, 0).
Since, C is equidistant from A and B.
∴ AC = BC

∴ The required point is (0, 3).

Q6. Establish the relation between x and y when P (x, y) is equidistant from the points A (− 1, 2) and B (2, − 1).

As P is equidistant from A and B
∴ PA = PB

which is the required relation.

Q7. Find a relation between x and y such that the point P (x, y) is equidistant from the points A (−5, 3) and B (7, 2) 

Since, P (x, y) is equidistant from A (−5, 3) and B (7, 2)
∴ AP = BP

Q8. In the given figure, ABC is a triangle. D and E are the mid points of the sides BC and AC respectively. Find the length of DE. Prove that 

Coordinates of the mid point of BC are:

Coordinates of the mid point of AC are:

Q9. Find the distance between the points  

Distance between   is given by

Q10. If the mid point of the line joining the points P (6, b − 2) and Q (− 2, 4) is (2, − 3), find the value of b.

Here, P (6, b − 2) and Q (− 2, 4) are the given points.
 ∴ Mid point of PQ is given by: