Question

Points A and B have co-ordinates (4, y) and (x, 8). The mid-point of AB = (0,0); the values of x and y are ______.

Options

• x = −4, y = 8

• x = 4, y = −8 

• x = −4, y = −8

• x = 4, y = 8

Answer 1

Points A and B have co-ordinates (4, y) and (x, 8). The mid-point of AB = (0,0); the values of x and y are x = −4, y = −8.

Explanation:

By mid-point formula,

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

Substituting values we get:

⇒ (0, 0) = `((4 + x)/2, (y + 8)/2)`

⇒ `(x + 4)/2 = 0 and (y + 8)/2 = 0`

⇒ x + 4 = 0 and y + 8 = 0

⇒x = −4 and y = −8.