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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?

AB(-4,-12)
BB(0,0)
CB(-4,12)
DB(23,33)

Verified Answer :

naǫ

The coordinates of the midpoint:
\((\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)
(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:
\(\frac{32+x}{2}=14 \ \ \ |\times 2 \\ 32+x=28 \ \ \ |-32 \\ x=-4\)

The y-coordinate of B:
\(\frac{40+y}{2}=26 \ \ \ |\times 2 \\ 40+y=52 \ \ \ |-40 \\ y=12\)

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

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