Question

18
AB has endpoint A(-2,3) and midpoint M(4,6).
Find the coordinates (x, y) of B.

Answer 1

B = (10, 9 )

Explanation:

Using the midpoint formula

M = (
`(x_(1)+x_(2) )/(2)`,
`(y_(1)+y_(2) )/(2)` )

with (x₁, y₁ ) = A(- 2, 3) and (x₂, y₂ ) = B(x, y) , then equate to the x and y coordinates of the midpoint M(4, 6)

`(-2+x)/(2)` = 4 ( multiply both sides by 2 )

- 2 + x = 8 ( add 2 to both sides )

x = 10

and

`(3+y)/(2)` = 6 ( multiply both sides by 2 )

3 + y = 12 ( subtract 3 from both sides )

y = 9

Then B = (10, 9 )