Question

name____ date____ you do 3 find the image of the point (5, 3) reflected in the line y = x you do 4/exit ticket triangle bcd has vertices b(-3, 3) c(1, 4) and d(-2, -4). find the coordinates of the vertices after a reflection in the line x = 3 you do 4 start with point b(-3, 3): then do point c(1, 4): last, do point d(-2, -4): finally, the three new vertices are:

Explanation:

Step1: Recall reflection rule for $y = x$

When a point $(x,y)$ is reflected in the line $y = x$, the coordinates are swapped. For the point $(5,3)$, the new - point is $(3,5)$.

Step2: Recall reflection rule for $x = 3$ for point B

The line $x = 3$ is a vertical line. The distance between $x=-3$ (x - coordinate of B) and $x = 3$ is $d=| - 3-3|=6$. The new x - coordinate of B after reflection in the line $x = 3$ is $x=3 + 6=9$, and the y - coordinate remains the same. So the new coordinates of B are $(9,3)$.

Step3: Recall reflection rule for $x = 3$ for point C

The distance between $x = 1$ (x - coordinate of C) and $x = 3$ is $d=|1 - 3|=2$. The new x - coordinate of C after reflection in the line $x = 3$ is $x=3+2 = 5$, and the y - coordinate remains the same. So the new coordinates of C are $(5,4)$.

Step4: Recall reflection rule for $x = 3$ for point D

The distance between $x=-2$ (x - coordinate of D) and $x = 3$ is $d=| - 2-3|=5$. The new x - coordinate of D after reflection in the line $x = 3$ is $x=3 + 5=8$, and the y - coordinate remains the same. So the new coordinates of D are $(8,-4)$.

Answer:

The image of the point $(5,3)$ reflected in the line $y = x$ is $(3,5)$.
The vertices of triangle BCD after reflection in the line $x = 3$ are B$(9,3)$, C$(5,4)$, D$(8,-4)$.