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 will be $(3,5)$.

Step2: Recall reflection rule for $x = 3$

For a point $(x,y)$ reflected in the line $x = a$, the formula for the new $x$ - coordinate is $x'=2a - x$ and the $y$ - coordinate remains the same.

For point B(-3,3):

$x'=2\times3-(-3)=6 + 3=9$, $y' = 3$. So the new point B' is $(9,3)$.

For point C(1,4):

$x'=2\times3 - 1=6 - 1=5$, $y' = 4$. So the new point C' is $(5,4)$.

For point D(-2,-4):

$x'=2\times3-(-2)=6 + 2=8$, $y'=-4$. So the new point D' is $(8,-4)$.

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), and D'(8,-4).