Question

a glide reflection is a composition of a refl

1. draw $(t_{(0,-2)}circ r_{p})(\triangle abc)$.

Explanation:

Step1: Reflect $\triangle ABC$ over the line $p$

Let's assume the line \(p\) is \(x = 4\).
For a point \((x,y)\) reflected over the line \(x=a\), the formula is \((2a - x,y)\).
For point \(A(4,-4)\):
\(x = 4,y=-4,a = 4\), then \(A'(2\times4 - 4,-4)=(4,-4)\) (since \(A\) is on the line \(x = 4\), it remains the same after reflection over \(x = 4\)).
For point \(B(4,4)\):
\(x = 4,y = 4,a=4\), then \(B'(4,4)\) (since \(B\) is on the line \(x = 4\), it remains the same after reflection over \(x = 4\)).
For point \(C(-2,4)\):
\(x=-2,y = 4,a = 4\), then \(C'(2\times4-(-2),4)=(10,4)\).

Step2: Translate the reflected triangle \((T_{(0,-2)})\)

The translation rule \(T_{(0,-2)}\) means \((x,y)\to(x,y - 2)\)
For \(A'(4,-4)\): \(A''(4,-4-2)=(4,-6)\)
For \(B'(4,4)\): \(B''(4,4 - 2)=(4,2)\)
For \(C'(10,4)\): \(C''(10,4-2)=(10,2)\)

Answer:

Plot the points \(A''(4,-6)\), \(B''(4,2)\) and \(C''(10,2)\) and connect them to form the triangle \((T_{(0,-2)}\circ r_{p})(\triangle ABC)\)