Question

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 ______.

Options

• (0, – 5) and (2, 0)

• (0, 10) and (– 4, 0)

• (0, 4) and (– 10, 0)

• (0, – 10) and (4, 0)

Answer 1

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).

Explanation:

Let the coordinates of P and 0 (0, y) and (x, 0), respectively.

So, the mid-point of P(0, y) and Q(x, 0) is `M((0 + x)/2, (y + 0)/2)`   ...`[∵  "Mid-point of a line segment having points"  (x_1, y_1)  "and"  (x_2, y_2) = ((x_1 + x_2)/2, (y_1 + y_2)/2)]`

But it is given that, mid-point of PQ is (2, –5).

∴ 2 = `(x + 0)/2`

And – 5 = `(y + 0)/2`

⇒ 4 = x and – 10 = y

⇒ x = 4 and y = – 10

So, the coordinates of P and Q are (0, – 10) and (4, 0).