Question

Points E(-1, -2) and F(4, -2) are the vertices of a square. Give the coordinates of three possible pairs of points for the other two vertices.

I already got the pairs:
(-1, 3), (4, 3)
(-1, -7), (4, -7)

I have no idea what to do for the third set of points.

Answer 1

The vertices of a square are its endpoints

The coordinates of the other pairs are: (-1, 3), (4, 3)  and (-1, -7), (4, -7)

The given parameters are:

$\mathbf{E = (-1,-2)}$

$\mathbf{F = (4,-2)}$

Calculate the distance EF

$\mathbf{EF = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

So, we have:

$\mathbf{EF = \sqrt{(-1 - 4)^2 + (-2 - -2)^2}}$

$\mathbf{EF = \sqrt{25}}$

$\mathbf{EF = 5}$

Add 5 to the y-coordinates of E and F

$\mathbf{C = (-1,-2+5)}$

$\mathbf{C = (-1,3)}$

$\mathbf{D = (4,-2+5)}$

$\mathbf{D = (4,3)}$

Subtract 5 to the y-coordinates of E and F

$\mathbf{C = (-1,-2-5)}$

$\mathbf{C = (-1,-7)}$

$\mathbf{D = (4,-2-5)}$

$\mathbf{D = (4,-7)}$

Hence, the coordinates of the other pairs are: (-1, 3), (4, 3)  and (-1, -7), (4, -7)

There is no third pair

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