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

Answer:

B(-2, -7)

Step-by-step explanation:

Midpoint is (0, -3)

A(x₁, y₁) B(x₂, y₂)

A(2, 1)

$Midpoint = (\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2} )\\\\Midpoint = (\frac{2+ x_{2} }{2}, \frac{1 + y_{2} }{2} )$

$(0, -3) = (\frac{2+ x_{2} }{2}, \frac{1 + y_{2} }{2} )$

              $\frac{2+ x_{2} }{2} = 0\\\\2 + x_{2} = 0\ \ \ \ times\ both\ sides\ by\ 2\\x_{2} = -2\ \ \ \ subtract\ both\ sides\ by\ 2$

              $\frac{1 + y_{2} }{2} = -3\\\\1 + y_{2} = -6\ \ \ \ times\ both\ sides\ by\ 2\\y_{2} = -7\ \ \ \ subtract\ both\ sides\ by\ 1$

∴ B(-2, -7)