Given triangle XYW with vertices X(2, b), Y(-4, -2) and W(-2, 3), the slope of a straight line is given by
[tex]m= \frac{y_2-y_1}{x_2-x_1} [/tex]
Thus, the slope of XY is given by
[tex] \frac{-2-b}{-4-2} =0.56 \\ \\ -2-b=0.56(-6)=-3.36 \\ \\ b=-2+3.36=1.36 [/tex],
Thus the vertex of X is (2, 1.36)
Therefore, the slope of WX is given by
[tex]\frac{1.36-3}{2-(-2)}= \frac{-1.64}{4} =-0.41[/tex],
and the slope of YW is given by
[tex]\frac{3-(-2)}{-2-(-4)}= \frac{3+2}{-2+4} = \frac{5}{2}=2.5[/tex].
For a right triangle, two of the sides intersect each other at 90 degrees (i.e. they are perpendicular to each other).
When two lines are perpendicular the product of the slopes of the the lines is -1. i.e. the slopes of two perpendicular lines are opposite reciprocal.
Two numbers are said to be opposite reciprocal when one of the number is the result of taking the reciprocal of the other number and then changing the sign.
Recall that the slope of WX is -0.41 and the slope of YW is 2.5, but 2.5 x (-0.41) ≈ -1.
Therefore, the statement that verifies that triangle WXY is a right triangle is "
The slopes of WX and YW are opposite reciprocals."
