Question

1. graph the images after the composition of transformations.

a) reflection in the x - axis
b) translation (x,y)→(x - 4,y + 2)
pre - i f( , ) p( , ) t( , )
reflection
translation

Explanation:

Step1: Identify pre - image coordinates

Assume from the graph, $F(0,4)$, $P(2,4)$, $T(2,2)$.

Step2: Apply reflection in the x - axis

The rule for reflection in the x - axis is $(x,y)\to(x, - y)$.
For $F(0,4)$: $(0,4)\to(0,-4)$
For $P(2,4)$: $(2,4)\to(2,-4)$
For $T(2,2)$: $(2,2)\to(2,-2)$

Step3: Apply translation

The translation rule is $(x,y)\to(x - 4,y + 2)$.
For the reflected point of $F(0,-4)$: $(0-4,-4 + 2)=(-4,-2)$
For the reflected point of $P(2,-4)$: $(2-4,-4 + 2)=(-2,-2)$
For the reflected point of $T(2,-2)$: $(2-4,-2 + 2)=(-2,0)$

Answer:

Pre - I	$F(0,4)$	$P(2,4)$	$T(2,2)$
Translation	$(-4,-2)$	$(-2,-2)$	$(-2,0)$