Question

If P(4, 3) is mid-point of line segment AB, then ______.

Options

• A = (6, 0), B = (0, 8)

• A = (8, 6), B = (8, 0)

• A = (6, 8), B = (0, 6)

• A = (8, 0) and B = (0, 6)

Answer 1

If P(4, 3) is mid-point of line segment AB, then A = (8, 0) and B = (0, 6).

Explanation:

From figure,

A lies on x-axis and B lies on y-axis.

Let co-ordinates of A be (x, 0) and B be (0, y).

Given,

P(4, 3) is mid-point of line segment AB.

By mid-point formula,

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

Substituting values we get:

⇒ (4,3) = `((x + 0)/2​, (0 + y)/2​)`

⇒ (4, 3) = `(x/2​, y/2​)`

⇒ `x/2​ = 4 and y/2 = 3`

⇒ x = 8 and y = 6

A = (x, 0) = (8, 0),

B = (0, y) = (0, 6)