Question

(05.02 MC)

Answer 1

Option C:

It is  $\frac{1}{3}$ throughout the line.

Solution:

Point on the larger shaded triangle are (0, 0) and (–6, –2).  

Point on the smaller shaded triangle are (–6, –2) and (–9, –3).

Slope of the line:

 $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Slope of the larger triangle:

Here,  $x_{1}=0, y_{1}=0, x_{2}=-6, y_{2}=-2$

 $m=\frac{-2-0}{-6-0}$

 $m=\frac{-2}{-6}$

 $m=\frac{1}{3}$  

Slope of the smaller triangle:

Here,  $x_{1}=-6, y_{1}=-2, x_{2}=-9, y_{2}=-3$

 $m=\frac{-3-(-2)}{-9-(-6)}$

 $m=\frac{-3+2}{-9+6}$

 $m=\frac{-1}{-3}$

 $m=\frac{1}{3}$

Both slopes are equal.

It is  $\frac{1}{3}$ throughout the line.

Hence option B is the correct answer.