Question

20 points.

The midpoint of AB is (-1, 5) and the coordinates of point A are (-3, 2) what are the coordinates of point B? ​

Answer 1

B (1, 8 )

Explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

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

with (x₁, y₁ ) = A (- 3, 2 ) and (x₂, y₂ ) = B (x, y )

Calculate the midpoint values and equate to the corresponding coordinates of the given midpoint (- 1, 5 ) , that is

`(-3+x)/(2)` = - 1 ( multiply both sides by 2 )

- 3 + x = - 2 ( add 3 to both sides )

x = 1

`(2+y)/(2)` = 5 ( multiply both sides by 2 )

2 + y = 10 ( subtract 2 from both sides )

y = 8

Then point B = (1, 8 )