Question

for items 3 - 5, use the information to answer each question. 3. quadrilateral c(3,6), d(5,2), e(2, - 1), f(-2, - 3) is reflected over the line y = 4 to form cdef. what are the coordinates of cdef? c: ( ) d: ( ) e: ( ) f: ( )

Explanation:

Step1: Recall reflection formula

When a point $(x,y)$ is reflected over the line $y = a$, the new - point $(x,y')$ has the formula $y'=2a - y$. Here $a = 4$.

Step2: Find coordinates of $C'$

For point $C(3,6)$, using the formula $y'=2\times4 - 6=8 - 6 = 2$. So $C'(3,2)$.

Step3: Find coordinates of $D'$

For point $D(5,2)$, using the formula $y'=2\times4 - 2=8 - 2 = 6$. So $D'(5,6)$.

Step4: Find coordinates of $E'$

For point $E(2, - 1)$, using the formula $y'=2\times4-(-1)=8 + 1 = 9$. So $E'(2,9)$.

Step5: Find coordinates of $F'$

For point $F(-2,-3)$, using the formula $y'=2\times4-(-3)=8 + 3 = 11$. So $F'(-2,11)$.

Answer:

$C':(3,2)$
$D':(5,6)$
$E':(2,9)$
$F':(-2,11)$