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The midpoint of a line segment is (4,2). If one of the endpoints is (-2,3), what is the other endpoint?

Sagot :

Answer:

(10, 1 )

Step-by-step explanation:

Using the midpoint formula

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then

midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Calculate the coordinates of midpoint and equate each to the given midpoint

(x₁, y₁ ) = - 2, 3), let coordinates of other endpoint = (x, y ) , then

[tex]\frac{-3+x}{2}[/tex] = 4 ( multiply both sides by 2 )

- 2 + x = 8 ( add 2 to both sides )

x = 10

and

[tex]\frac{3+y}{2}[/tex] = 2 ( multiply both sides by 2 )

3 + y = 4 ( subtract 3 from both sides )

y = 1

coordinates of other endpoint are (10, 1 )

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