Question

what is the reflection rule for the triangle and image with coordinates a(2,4), b(4,5), c(5,3) and a(-2,4), b(-4,5), c(-5,3)? the reflection rule is r_m(abc)→ where m is the line. (type an equation. simplify your answer.)

Explanation:

Step1: Analyze coordinate - change pattern

We observe that for point A(2,4) and its image A'(-2,4), the x - coordinate changes sign while the y - coordinate remains the same. The same pattern holds for B(4,5) and B'(-4,5), and C(5,3) and C'(-5,3).

Step2: Determine reflection line

The reflection that changes the sign of the x - coordinate and keeps the y - coordinate the same is a reflection over the y - axis. The equation of the y - axis is x = 0. The general rule for a reflection over the y - axis for a point (x,y) is (x,y)→(-x,y). So for a triangle ABC with vertices (x,y) coordinates, the reflection rule \(r_{m}(ABC)\to A'B'C'\) where \(m\) is the line \(x = 0\) is \(r_{x = 0}(x,y)\to(-x,y)\).

Answer:

\(r_{x = 0}(x,y)\to(-x,y)\)