Question

triangle def has coordinates d(4, -1), e(5, 2), and f(1, 2). determine the coordinates of the vertices of the image after a reflection in the y - axis.

a) d(4, 1), e(5, -2), and f(1, -2)
b) d(5, -1), e(6, 2), and f(2, 2)
c) d(-4, -1), e(-5, 2), and f(-1, 2)
d) d(1, 0), e(2, 3), and f(-2, 3)

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ in the $y$-axis, the rule is $(x,y)\to(-x,y)$.

Step2: Apply rule to point D

For point $D(4, - 1)$, applying the rule gives $D'(-4,-1)$ since $x = 4$ becomes $-4$ and $y=-1$ remains the same.

Step3: Apply rule to point E

For point $E(5,2)$, applying the rule gives $E'(-5,2)$ as $x = 5$ becomes $-5$ and $y = 2$ stays the same.

Step4: Apply rule to point F

For point $F(1,2)$, applying the rule gives $F'(-1,2)$ as $x = 1$ becomes $-1$ and $y = 2$ is unchanged.

Answer:

C. $D'(-4,-1), E'(-5,2),$ and $F'(-1,2)$