Question

Determine if triangle XYZ with coordinates X (1, 1), Y (5, 6), and Z (6, 2) is a right triangle. Use evidence to support your claim. If it is not a right triangle, what changes can be made to make it a right triangle? Be specific.

Answer 1

We will use the formula for distance;

XY = $\sqrt{ ( x_{Y}- x_{X} )^{2}+y_{Y}- y_{X} )^{2} } = \sqrt{ (1-5 )^{2}+(1-6 )^{2} } = \sqrt{ 16+25 } = \sqrt{41}$
Applying the same formula
YZ = $\sqrt{17}$
XZ = $\sqrt{26}$

XZ^2 + YZ^2 is not equal with XY^2 which means the triangle is not right.

In order to make the triangle right, we have to take X and Z on the same x-line which means Z will be (6, 1) and Z and Y to be on the same y-line which means Y will be (6, 6). The point will be:
X(1, 1)
Y(6, 6)
Z(6, 1)

XY = $\sqrt{50}$
YZ = $\sqrt{25}$
XZ = $\sqrt{25}$

It means that: YZ^2+XZ^2=XY^2 and the triangle is right.