Question

Ms. Issa is building a rectangular fish pond in her garden. A drawing shows three corners of the pond with coordinates (4, -2), (-2, -2), and (-2, -5) where is the 4th corner

Answer 1

The answer to your question is: (4, -5)

Explanation:

Data

(4, -2)

(-2, -2)

(-2, -5)

4th corner

See the graph below

Answer 2

(4, -5)

Explanation:

It can be helpful to plot the points. (See the attachment)

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There are several other ways you can get there.

Once you recognize that x-coordinates and y-coordinates are repeated in adjacent vertices, you realize the line segments are aligned with the axes. That means each coordinate value will show up in two (2) adjacent vertices. The coordinates that are missing are x=4 and y=-5, so you know the missing vertex is (4, -5).

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In a rectangle, the two diagonals bisect each other. That means their midpoints are the same. The midpoint of diagonal AC is (A+C)/2, and the midpoint of diagonal BD is (B+C)/2. Equating these points, we find ...

(A+C)/2 = (B+D)/2

A+C = B+D

A+C-B = D

The fourth point can be found using this formula. So ...

D = (4, -2) +(-2, -5) -(-2, -2) = (4-2+2, -2-5+2)

D = (4, 5)