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The midpoint of line AB is (14,26). One endpoint of line AB is A(32, 40). What are the coordinates of B?
A. B(-4,-12)
B. B(0,0)
C. B(-4,12)
D. B(23,33)

Sagot :

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The coordinates of the midpoint:
[tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
(x₁,y₁) - the coordinates of one endpoint
(x₂,y₂) - the coordinates of the other endpoint

The midpoint is (14,26).
One endpoint is A(32,40).
The other endpoint is B.

The x-coordinate of B:
[tex]\frac{32+x}{2}=14 \ \ \ |\times 2 \\ 32+x=28 \ \ \ |-32 \\ x=-4[/tex]

The y-coordinate of B:
[tex]\frac{40+y}{2}=26 \ \ \ |\times 2 \\ 40+y=52 \ \ \ |-40 \\ y=12[/tex]

The coordinates of B are (-4,12) - the answer is C.
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