Question

MAKE CONNECTIONS Determine whether triangle XYZ can be a right triangle. Explain.

X (0, 0), Y (2h, 2h), Z (4h, 0)
Slope of XY Select Choice -1, 1, or 0
slope of YZ Select Choice 1, 0, or -1slope of ZX Select Choice -1, 1, or 0because Select Choice 1(1) = 1, 1(-1) = -1, 1(0) = 0, or 0(-1) =0XY Select Choice is or is not
perpendicular to YZ. Therefore, triangle XYZ Select Choice is not or is a right triangle.

Answer 1

Answer: slope of XY is not perpendicular to YZ. Therefore, triangle XYZ is a right triangle.

Explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).

Using this formula, we can find the slopes of the three sides of triangle XYZ:

Slope of XY = (2h - 0) / (2h - 0) = 1

Slope of YZ = (0 - 2h) / (4h - 2h) = -h / h = -1

Slope of ZX = (0 - 0) / (4h - 0) = 0

Therefore, the slope of XY is 1, the slope of YZ is -1, and the slope of ZX is 0.

Since the product of the slopes of two perpendicular lines is -1, we can see that the slope of XY and the slope of YZ are negative reciprocals of each other, which means that they are perpendicular. Therefore, triangle XYZ is a right triangle.