draw the line of reflection that reflects quadrilateral $abcd$ onto quadrilateral $abcd$.
draw the line of reflection that reflects quadrilateral $abcd$ onto quadrilateral $abcd$.
Answer
Explanation:
Step1: Identify corresponding points
Take point $A(0,4)$ and its image $A'(-6,-2)$; point $C(3,0)$ and its image $C'(-3,-6)$.
Step2: Find midpoint of $A$ and $A'$
Midpoint formula: $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$ $\left(\frac{0+(-6)}{2},\frac{4+(-2)}{2}\right)=(-3,1)$
Step3: Find midpoint of $C$ and $C'$
$\left(\frac{3+(-3)}{2},\frac{0+(-6)}{2}\right)=(0,-3)$
Step4: Calculate line slope
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$ $m=\frac{-3-1}{0-(-3)}=\frac{-4}{3}$
Step5: Write line equation
Use point-slope form $y-y_1=m(x-x_1)$ with $(0,-3)$: $y - (-3) = -\frac{4}{3}(x-0)$ Simplify to $y=-\frac{4}{3}x - 3$, or $4x+3y+9=0$
Answer:
The line of reflection is $\boldsymbol{4x + 3y + 9 = 0}$ (or $\boldsymbol{y = -\frac{4}{3}x - 3}$), which can be drawn by plotting two points from the equation (e.g., $(-3,1)$ and $(0,-3)$) and connecting them.