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

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

3 =
`(-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 =
`(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