A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
a. (0, – 5) and (2, 0)
b. (0, 10) and (– 4, 0)
c. (0, 4) and (– 10, 0)
d. (0, – 10) and (4, 0)

Solution:

We know that

The coordinates of the mid-point of the line segment joining the point are

[(x₁ + x₂)/2, (y₁ + y₂)/2]

Consider the coordinates of P as (x, y) and Q as (x₂, y₂)

The midpoint of PQ = (2, -5)

Using the midpoint formula

x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2

2 = (x₁ + x₂)/2 and -5 = (y₁ + y₂)/2

By cross multiplication

x₁ + x₂ = 4

y₁ + y₂ = -10

As the line PQ intersects the Y-axis at P

x₁ = 0

In the same way, y₂ = 0

x₂ = 4 and y₁ = -10

So the coordinates of P is (0, -10) and Q is (4, 0).

Therefore, the coordinates of P and Q are (0, -10) and (4, 0).

✦ Try This: A line intersects the y-axis and x-axis at the points A and B, respectively. If (3, -6) is the mid-point of AB, then the coordinates of A and B are, respectively

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.1 Problem 17

A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively a. (0, – 5) and (2, 0), b. (0, 10) and (– 4, 0), c. (0, 4) and (– 10, 0), d. (0, – 10) and (4, 0)

Summary:

A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively (0, – 10) and (4, 0)

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