Question

d)reflect △tab if t(2,3), a(1,1), and b(4,-3) over the y - axis, then translate the image by moving it right 2 and down 1. f)reflect △tab if t(2,3), a(1,1), and b(4,-3) over the x - axis, then translate the image by moving it left 5 and down

Explanation:

Step1: Reflect over y - axis

The rule for reflecting a point $(x,y)$ over the y - axis is $(-x,y)$.
For point $T(2,3)$, the reflection $T_1$ is $(- 2,3)$.
For point $A(1,1)$, the reflection $A_1$ is $(-1,1)$.
For point $B(4,-3)$, the reflection $B_1$ is $(-4,-3)$.

Step2: Translate right 2 and down 1

The rule for translating a point $(x,y)$ right 2 and down 1 is $(x + 2,y-1)$.
For $T_1(-2,3)$, the new point $T_2$ is $(-2 + 2,3-1)=(0,2)$.
For $A_1(-1,1)$, the new point $A_2$ is $(-1 + 2,1-1)=(1,0)$.
For $B_1(-4,-3)$, the new point $B_2$ is $(-4 + 2,-3-1)=(-2,-4)$.

Answer:

The new coordinates of $\triangle TAB$ are $T(0,2)$, $A(1,0)$, $B(-2,-4)$