Question

The line AB has midpoint (-2, 4).A has coordinates (3,-2).Find the coordinates of B.​

Answer 1

Answer: B(8, -8 )

Step-by-step explanation: The formula for calculating mid - point between two points is given as :

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

The mid point has been given from the question .

$x_{1}$ = -2

$x_{2}$ = ?

$y_{1}$ = 4

$y_{2}$ = ?

substituting into the formula , we have

(3 , - 2 ) = ($\frac{-2+x_{2}}{2}$ , $\frac{4+y_{2}}{2}$ )

Equating x -component to x and y component to y , we have

3 = $\frac{-2+x_{2}}{2}$

cross multiplying , we have

6 = -2 + $x_{2}$

Therefore:

$x_{2}$ = 8

Also , equating y component to y , we have

-2 = $\frac{4+y_{2}}{2}$

-4 = 4 + $y_{2}$

$y_{2}$ = -8

Therefore :

$x_{2}$  = 8

$y_{2}$  = -8

check

-2 + 8 / 2 = 3 and

-8 + 4 / 2 = -2