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

Answer:

• F(8, 6)

Step-by-step 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

Answer 2

Using Midpoint formula

$\boxed{\sf M=\dfrac{x_1+x_2}{2},\dfrac{x_2+y_2}{2}}$

• E(-7,2)
• M(0.5,4)
• F(x,y)

$\\ \sf\longmapsto (0.5,4)=\left(\dfrac{-7+x}{2},\dfrac{2+y}{2}\right)$

$\\ \sf\longmapsto \dfrac{-7+x}{2}=0.5$

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

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

$\\ \sf\longmapsto x=8$

And

$\\ \sf\longmapsto \dfrac{2+y}{2}=4$

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

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

$\\ \sf\longmapsto y=6$

• F(x,y)=(8,6)