Question

A rectangle has verticles at these coordinates (-6, 3), (-6, 5), (2, 3)

What are the coordinates of the fourth vortex of the rectangle?

Answer 1

Answer: (2,5)

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Answer 2

the fourth vertex is D(2,5).

Explanation:

A rectangle has vertices at these coordinates A(-6, 3), B(-6, 5), C(2, 3).

Suppose the fourth vertex is D(x, y).

Then to make a rectangle, AB = CD.

√{(-6 - -6)² + (5 - 3)²} = √{(x-2)² + (y-3)²}.

√{(-6 + 6)² + (5 - 3)²} = √{(x-2)² + (y-3)²}.

√{(0)² + (2)²} = √{(x-2)² + (y-3)²}.

So x-2=0 and y-3=2

x=2 and y=5.

Hence, the fourth vertex is D(2,5).