Question

The midpoint of AB is M (0, -3). If the coordinates of AA are (2, 1) what are the coordinates of BB?

Answer 1

B(-2, -7)

Explanation:

Midpoint is (0, -3)

A(x₁, y₁) B(x₂, y₂)

A(2, 1)

`Midpoint = ((x_(1) + x_(2) )/(2), (y_(1) + y_(2) )/(2) )\\\\Midpoint = ((2+ x_(2) )/(2), (1 + y_(2) )/(2) )`

`(0, -3) = ((2+ x_(2) )/(2), (1 + y_(2) )/(2) )`

`(2+ x_(2) )/(2) = 0\\\\2 + x_(2) = 0\ \ \ \ times\ both\ sides\ by\ 2\\x_(2) = -2\ \ \ \ subtract\ both\ sides\ by\ 2`

`(1 + y_(2) )/(2) = -3\\\\1 + y_(2) = -6\ \ \ \ times\ both\ sides\ by\ 2\\y_(2) = -7\ \ \ \ subtract\ both\ sides\ by\ 1`

∴ B(-2, -7)