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Find the coordinates of the missing endpoint if Wis the MIDPOINT of XY.
Y(2,9) W(-1,6)

Find The Coordinates Of The Missing Endpoint If Wis The MIDPOINT Of XY Y29 W16 class=

Sagot :

oladayoademosu

The coordinates of the missing endpoint are (-4, 3)

The coordinates of the midpoint of a line (x,y) is given by x =

[tex]x = \frac{x_{1} + x_{2}}{2}[/tex] and [tex]y = \frac{y_{1} + y_{2}}{2}[/tex] where (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints of the line.

Given that the midpoint of the line XY is W = (-1, 6) and one endpoint Y = (2, 9), the missing endpoint is X = (x₁, y₁).

Making x₁ and y₁ the subject of the formula in the equation for x and y, we have

x₁ = 2x - x₂ and y₁ = 2y - y₂

Since the midpoint is W = (-1,6), (x, y) = (-1, 6) and the other endpoint is Y = (2, 9 ). So, (x₂, y₂) = (2, 9)

So, x = -1 and x₂ = 2

Substituting the values of the variables into the expression for x₁, we have

x₁ = 2x - x₂

x₁ = 2(-1) - 2

x₁ = -2 - 2

x₁ = -4

Also, y = 6 and y₂ = 9

Substituting the values of the variables into the expression for y₁, we have

y₁ = 2y - y₂

y₁ = 2(6) - 9

y₁ = 12 - 9

y₁ = 3

Since x₁ = -4 and y₁ = 3,

The coordinates of the missing endpoint are (-4, 3)

Learn more about coordinates of endpoint here:

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