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)
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