Question

The kitchen in Tina's house is a square. The points P(6, -1) and Q(0, 3) represent the opposite vertices of her kitchen in a drawing on a coordinate grid. Which of these ordered pairs could be a third vertex?

( I am so lost on this one. )

Answer 1

( 5, 5)

( 3, 6 )

(1, -1)

(1, -2)

Please explain, I do not understand.

Answer 2

It is (1, -2).

This is how:
You are given the opposite vertices of the square. By using the Distance Formula, you can obtain the distance between these two points, which would be a diagonal, since the points are opposite vertices. Use the formula \[\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 }\]

and you'll see the distance between the two points is square root of 52. Now, you can use Pythagorean Theorem to calculate the size of an edge of this square. You have the size of the diagonal, which forms a right-angled triangle of which it is the hypotenuse. You'll see the size of an edge is square root of 26.

Use the distance formula again by choosing each of the given options as the second point and one of the given vertices are the first, to find out which one equals square root of 26. I used (6, -1).