A student draws three vertices of a square on the coordinate plane. The three vertices are X ( − 10 , − 1 ) , Y ( − 10 , 5 ) , and Z ( − 4 , − 1 ) . Which coordinate pair could be the fourth vertex of the square?

There are different types of quadrilaterals, for example: square, rectangle, rhombus and trapezoid. Each type is defined accordingly to its length of sides and angles. For example, the square has all side equals and angles equal to 90°.

For solving this question, you should plot the given points as shown in attached image. Note that you have only two sides of a square, and you need a point (W) for completing the square.

As you have a square, all sides should have the same dimensions and all angles should equal to 90°. Therefore, the coordinates for the point W should result in equal and parallel sides XY and XZ. For this, from the attached image, you can see that the x-coordinate for the point W should be equal to the x-coordinate for the point Z. And, the y-coordinate for the point W should be equal to the y-coordinate for the point Y.

Thus, coordinate pair (-4,5) would be the fourth vertex of the square.

Read more about the quadrilaterals here:

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