Question

Which statement verifies that triangle WXY is a right triangle?

The slopes of WX and YW are opposite reciprocals.
The slopes of WX and XY are opposite reciprocals.
The slopes of XY and WX have opposite signs.
The slopes of XY and YW have the same signs

Answer 1

The slopes of WX and YW are opposite reciprocals.

Answer 2

The statement is slope of WX and YW are opposite reciprocals

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=(y_2-y_1)/(x_2-x_1)`

`\text{Slope of WX=}(1.4-3)/(2-(-2))=(-2)/(5)`

`\text{Slope of XY=}(-2-1.4)/(-4-2)=(17)/(30)`

`\text{Slope of YW=}(-2-3)/(-4-(-2))=(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