Question

Point A lies on x-axis and point B lies on y-axis. If P(2, −2) bisects the line segment AB, the co-ordinates of A are ______.

Options

• (4, 0)

• (0, 4)

• (−4, 0)

• (0, −4)

Answer 1

Point A lies on x-axis and point B lies on y-axis. If P(2, −2) bisects the line segment AB, the co-ordinates of A are (4, 0).

Explanation:

Given,

Point A lies on x-axis.

∴ Let point A be (x, 0).

Point B lies on y-axis.

∴ Let point B be (0, y).

P(2, −2) bisects the line segment AB or P is the mid-point of AB.

By mid-point formula,

Mid-point = `((x_1+x_2)/22, (y_1+y_2)/2)`

Substituting values we get:

⇒ (2, −2) = `((x + 0)/2, (0 + y)/2)`

⇒ (2, −2) = `(x/2, y/2)`

⇒ `x/2 = 2 and y/2 = -2`

⇒ x = 4 and y = −4

Co-ordinates of A = (x, 0) = (4, 0)