Question

A line intersects y-axis and x-axis at point P and Q, respectively. If R(2, 5) is the mid-point of line segment PQ, them find the coordinates of P and Q.

Answer 1

Let P point be (0, y)

and Q point be (x, 0)

Since, on y-axis, x = 0 and on x-axis, y = 0

Let coordinates of point P be (0, y)

and coordinates of point Q be (x, 0)

Since, mid-point of points (x₁, y₁) and (x₂, y₂) is

`((x_1 + x_2)/2, (y_1 + y_2)/2)`

∴ 2 = `(0 + x)/2 \implies` x = 4

and 5 = `(y + 0)/2 \implies` y = 10

∴ coordinates of P = (0, 10)

and coordinates of Q = (4, 0)