First, second and fourth options are true about triangle XYZ.
XY measures [tex]\sqrt{26}[/tex] units.
YZ measures [tex]\sqrt{52}[/tex] units.
ZX measures [tex]\sqrt{26}[/tex] units.
XYZ is a right triangle.
A triangle in which one of the interior angles is 90° is called a right triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the height and the base.
Given X (-1, 5), Y (4, 4), Z (-2, 0)
Distance between two points D = [tex]\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1}) ^{2}}[/tex]
|XY| = [tex]\sqrt{(4-5)^{2} +(4+1)^{2} } =\sqrt{1^{2}+5^{2} } =\sqrt{26}[/tex]
|YZ| = [tex]\sqrt{(0-4)^{2} +(-2-4)^{2} } =\sqrt{4^{2}+6^{2} } =\sqrt{52}[/tex]
|XZ| = [tex]\sqrt{(0-5)^{2} +(-2+1)^{2} } =\sqrt{5^{2}+1^{2} } =\sqrt{26}[/tex]
[tex]|XY|^{2} +|XZ|^{2} =|YZ|^{2}[/tex]
So, XYZ is a right triangle.
So, the first, second and fourth options are correct.
Find out more information about right triangle here
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