The product of the slope of XZ and XY is -1, and XZ = XY = 5. Hence. triangle XYZ is the right isosceles triangle.
If a triangle is right isosceles triangle, then it must have one angle of 90 degrees and two equal sides that is corresponding to that right angle.
If two lines are perpendicular to each other, then the product of the slope of the perpendicular lines must be equal to - 1.
The formula for finding the slope of the line from two known points is given as;
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line.
Solving for the slopes of XZ and XY:
Slope of XZ = (y₂-y₁) / (x₂-x₁) = (6-3)/(5-1) = 3/4
Slope of XY = (y₂-y₁) / (x₂-x₁) = (3--1)/(1-4) = -4/3
Thus, the product of the slopes of XY and XZ is -1. Hence, both sides made an angle of 90 degrees.
Solving for distance:
XZ = √[(y₂-y₁)²+(x₂-x₁)²] = √[(6-3)²+(5-1)²] = 5
XY = √[(y₂-y₁)²+(x₂-x₁)²] = √[(3--1)²+(1-4)²] = 5
The product of the slope of XZ and XY is -1, and XZ = XY = 5. Hence. triangle XYZ is the right isosceles triangle.
To know more about the right isosceles triangle, please refer to the link:
https://brainly.com/question/21881466
