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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

Sagot :

mhanifa

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

Using Midpoint formula

[tex]\boxed{\sf M=\dfrac{x_1+x_2}{2},\dfrac{x_2+y_2}{2}}[/tex]

  • E(-7,2)
  • M(0.5,4)
  • F(x,y)

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

[tex]\\ \sf\longmapsto \dfrac{-7+x}{2}=0.5[/tex]

[tex]\\ \sf\longmapsto -7+x=1[/tex]

[tex]\\ \sf\longmapsto x=1+7[/tex]

[tex]\\ \sf\longmapsto x=8[/tex]

And

[tex]\\ \sf\longmapsto \dfrac{2+y}{2}=4[/tex]

[tex]\\ \sf\longmapsto y+2=8[/tex]

[tex]\\ \sf\longmapsto y=8-2[/tex]

[tex]\\ \sf\longmapsto y=6[/tex]

  • F(x,y)=(8,6)
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