Question

Segment EF has one endpoint located at E (-7, 2) and its midpoint is located at M (0.5, 4). What are the coordinates of point F? Show all work.

100 POINTS

Answer 1

Using Midpoint formula

`\boxed{\sf M=(x_1+x_2)/(2),(x_2+y_2)/(2)}`

• E(-7,2)
• M(0.5,4)
• F(x,y)

`\\ \sf\longmapsto (0.5,4)=\left((-7+x)/(2),(2+y)/(2)\right)`

`\\ \sf\longmapsto (-7+x)/(2)=0.5`

`\\ \sf\longmapsto -7+x=1`

`\\ \sf\longmapsto x=1+7`

`\\ \sf\longmapsto x=8`

And

`\\ \sf\longmapsto (2+y)/(2)=4`

`\\ \sf\longmapsto y+2=8`

`\\ \sf\longmapsto y=8-2`

`\\ \sf\longmapsto y=6`

• F(x,y)=(8,6)

Answer 2

• F(8, 6)

Explanation:

Use midpoint formula to find the missing F(x, y):

• M = (E + F)/2
• (-7 + x)/2 = 0.5 ⇒ -7 + x = 1 ⇒ x = 1 + 7 = 8
• (2 + y)/2 = 4 ⇒ 2 + y = 8 ⇒ y = 8 - 2 = 6