Question

what are the coordinates of the image after the reflection in the given line. x = -1 a() b() c()

Explanation:

Step1: Recall reflection rule

For reflection over $x = a$, the rule is $(x,y)\to(2a - x,y)$. Here $a=-1$.

Step2: Find A'

The coordinates of A are (2, -2). Using the rule, $x'=2\times(-1)-2=-2 - 2=-4$, $y'=-2$. So A' is (-4, -2).

Step3: Find B'

The coordinates of B are (-3, 1). Using the rule, $x'=2\times(-1)-(-3)=-2 + 3 = 1$, $y'=1$. So B' is (1, 1).

Step4: Find C'

The coordinates of C are (2, 3). Using the rule, $x'=2\times(-1)-2=-2 - 2=-4$, $y'=3$. So C' is (0, 3).

Answer:

A'(-4, -2)
B'(1, 1)
C'(0, 3)