Solution:
Given:
A coordinate plane with two similar triangles.
To get the slope of HI, because the two triangles are similar, their hypotenuses will always have the same slope.
Hence, the slope of HI is also the slope of DE.
[tex]\begin{gathered} \text{Considering }\Delta DEF,\text{ using the points (8,32) and (12,24)} \\ \text{where;} \\ x_1=8 \\ y_1=32 \\ x_2=12 \\ y_2=24 \end{gathered}[/tex]
Using the formula for calculating slope (m),
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the values of the points gotten from triangle DEF,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{24-32}{12-8} \\ m=\frac{-8}{4} \\ m=-2 \end{gathered}[/tex]
Since the slope of triangle DEF is the hypotenuse of the right triangle DEF, then the slope HI is also the hypotenuse of triangle HIJ and both hypotenuses have the same slope since both triangles are similar.
Therefore, the slope of HI is -2.
