Question

Given that point A is the midpoint of line segment ED, where E( -1,9) and A(4,5), what is the location of point D?

Answer 1

D(9, 1)

Step-by-step explanation:

Since A is the midpoint of ED, then;

A = (
`(X_(1)+X_(2) )/(2)`,
`(Y_(1)+Y_(2) )/(2)`)

A(4, 5) ⇒ 4 =
`(X_(1)+X_(2) )/(2)` and 5 =
`(Y_(1)+Y_(2) )/(2)`

`(X_(1)+X_(2) )/(2)` = 4

`X_(1)` +
`X_(2)` = 8

But
`X_(1)` = -1, then;

-1 +
`X_(2)` = 8

`X_(2)` = 9

`(Y_(1)+Y_(2) )/(2)` = 5

`Y_(1)` +
`Y_(2)` = 10

But
`Y_(1)` = 9, then;

9 +
`Y_(2)` = 10

`Y_(2)` = 1

Therefore, point D has coordinates (9, 1).