Question

Which statement verifies that triangle WXY is a right triangle?

Answer 1

The slopes of WX and YW are opposite reciprocals.

Answer 2

Answer:

The statement is slope of WX and YW are opposite reciprocals

Step-by-step explanation:

Given the graph in which triangle is shown

we have to choose the statement that verifies that triangle WXY is a right triangle.

Coordinates of W, X and Y are

W=(-2,3)

X=(2,1.4)

Y=(-4,-2)

To verify the triangle WXY a right triangle, we have to find the slope of these lines

$\text{Slope of line joining the points }(x_1,y_1), (x_2, y_2)\text{ is }$

$slope=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope of WX=}\frac{1.4-3}{2-(-2)}=\frac{-2}{5}$

$\text{Slope of XY=}\frac{-2-1.4}{-4-2}=\frac{17}{30}$

$\text{Slope of YW=}\frac{-2-3}{-4-(-2)}=\frac{5}{2}$

We see slope of WX and YW are opposite reciprocals that means these two lines are perpendicular which verifies that triangle WXY is a right triangle.

Hence, option 1 is correct