Question

part b. the vertices are s(0, - 3), t(-2, - 5), u(3, - 5), and v(2, - 3). draw the figure and its reflection in the line x = 1.

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ over the line $x = a$ is $(2a - x,y)$. Here $a = 1$.

Step2: Reflect point S

For $S(0,-3)$, using the rule $x'=2\times1 - 0=2$, $y'=-3$. So the image $S'(2,-3)$.

Step3: Reflect point T

For $T(-2,-5)$, $x'=2\times1-(-2)=4$, $y'=-5$. So the image $T'(4,-5)$.

Step4: Reflect point U

For $U(3,-5)$, $x'=2\times1 - 3=-1$, $y'=-5$. So the image $U'(-1,-5)$.

Step5: Reflect point V

For $V(2,-3)$, $x'=2\times1 - 2=0$, $y'=-3$. So the image $V'(0,-3)$.

Answer:

The original points are $S(0,-3),T(-2,-5),U(3,-5),V(2,-3)$ and their reflections over the line $x = 1$ are $S'(2,-3),T'(4,-5),U'(-1,-5),V'(0,-3)$. To draw, first plot the original points $S,T,U,V$ on the coordinate - plane, then plot the reflected points $S',T',U',V'$ and connect the corresponding points to show the original figure and its reflection.