Question

The red line makes up one side of the trapezoid above. If this line has a slope of
$\frac{3}{2}$, find the slope of the line after reflecting the trapezoid taking the x-axis as the line of reflection.

• A. $-\frac{2}{3}$
• B. $-\frac{3}{2}$
• C. $\frac{2}{3}$
• D. $\frac{3}{2}$

Answer 1

The correct option is B $-\frac{3}{2}$

The graph is symmetric(reflection) w.r.t to the $x$-axis i.e. $y=0$ , If $(x,y)$ is a point on the graph ,then $(x,-y)$ is also a point on the graph .

In the given figure ,point $A$ is situated at $(-5,2)$ ,then point $A^{{}^{\prime }}$ must be situated at $(-5,-2)$ .

similarly point $B$ is situated at $(-3,5)$ ,then point $B^{{}^{\prime }}$ must be situated at $(-3,-5)$ .

similarly for point $C$ and $D$,point $C^{{}^{\prime }}$ must be situated at $(2,-5)$ and point $D^{{}^{\prime }}$ must be situated at $(2,-2)$.

now the slope of the reflected red line about $X$-axis is

$m=(\frac{y_2-y_1}{x_2-x_1})$

here $y_1=-2$, $x_1=-5$

and $y_2=-5$, $x_2=-3$

now $m=(\frac{-5-(-2)}{-3-(-5)})$

hence $m=\frac{-3}{2}$