Question

Point M(5, 2) is the midpoint of segment XY. Point X has coordinates

(-4, 6). Find the coordinates of point Y

Please help!

Answer 1

Y (14, - 2 )

Explanation:

using the midpoint formula for (x₁, y₁ ) and (x₂, y₂ ) , then

midpoint = (
`(x_(1)+x_(2) )/(2)` ,
`\frac{y_{1+y_(2) } }{2}` )

equating the x- coordinates and the y- coordinates

let coordinates of Y = (x, y )

`(x-4)/(2)` = 5 ( multiply both sides by 2 )

x - 4 = 10 ( add 4 to both sides )

x = 14

and

`(y+6)/(2)` = 2 ( multiply both sides by 2 )

y + 6 = 4 ( subtract 6 from both sides )

y = - 2

coordinates of Y = (14, - 2 )

Answer 2

(14, -2)

Explanation:

The coordinates of the midpoint is equal to the mean of the coordinates of the endpoints.

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Solving :

⇒ 5 = -4 + x / 2

⇒ x - 4 = 10

⇒ x = 14

⇒ 2 = 6 + y / 2

⇒ y + 6 = 4

⇒ y = -2

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Coordinates of Point Y :

⇒ Y = (x, y)

⇒ Y = (14, -2)