Question

for exercises 25 - 28, what is a reflection rule that maps each triangle and its image? see example 4 25. d(3, 6), e(-4, -3), f(6, 1) and d(1, 6), e(8, -3), f(-2, 1) 26. g(9, 12), h(-2, -15), j(3, 8) and g(9, -2), h(-2, 25), j(3, 2)

Explanation:

Step1: Analyze x - coordinates for 25

For point $D(3,6)$ and $D'(1,6)$, $E(-4, - 3)$ and $E'(8,-3)$, $F(6,1)$ and $F'(-2,1)$. The y - coordinates remain the same. Let the line of reflection be $x = a$. The mid - point of the line segment joining a point and its image lies on the line of reflection. For $D$ and $D'$, the mid - point of the line segment $DD'$ has x - coordinate $\frac{3 + 1}{2}=2$. So the reflection rule is $x = 2$, or $(x,y)\to(4 - x,y)$.

Step2: Analyze y - coordinates for 26

For point $G(9,12)$ and $G'(9,-2)$, $H(-2,-15)$ and $H'(-2,25)$, $J(3,8)$ and $J'(3,2)$. The x - coordinates remain the same. Let the line of reflection be $y = b$. The mid - point of the line segment joining a point and its image lies on the line of reflection. For $G$ and $G'$, the mid - point of the line segment $GG'$ has y - coordinate $\frac{12+( - 2)}{2}=5$. So the reflection rule is $y = 5$, or $(x,y)\to(x,10 - y)$.

Answer:

1. $(x,y)\to(4 - x,y)$
2. $(x,y)\to(x,10 - y)$