We will use the formula for distance;
XY = [tex] \sqrt{ ( x_{Y}- x_{X} )^{2}+y_{Y}- y_{X} )^{2} } = \sqrt{ (1-5 )^{2}+(1-6 )^{2} } = \sqrt{ 16+25 } = \sqrt{41} [/tex]
Applying the same formula
YZ = [tex] \sqrt{17} [/tex]
XZ = [tex] \sqrt{26} [/tex]
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 = [tex] \sqrt{50} [/tex]
YZ = [tex] \sqrt{25} [/tex]
XZ = [tex] \sqrt{25} [/tex]
It means that: YZ^2+XZ^2=XY^2 and the triangle is right.
