Question

b)reflect △tab if t(2,3), a(1,1), and b(4,-3) over the x - axis, then reflect the image over the y - axis.

Explanation:

Step1: Reflect over x - axis

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

Step2: Reflect the new - points over y - axis

The rule for reflecting a point $(x,y)$ over the y - axis is $(-x,y)$.
For point $T_1(2,-3)$, the final image $T_2$ is $(-2,-3)$.
For point $A_1(1,-1)$, the final image $A_2$ is $(-1,-1)$.
For point $B_1(4,3)$, the final image $B_2$ is $(-4,3)$.

Answer:

The new coordinates of the vertices of the triangle are $T(-2,-3)$, $A(-1,-1)$, $B(-4,3)$