Question

determine a series of transformations that would map figure $l$ onto figure $m$.

Explanation:

Step1: Identify key vertices

Figure L vertices: $(5,-1)$, $(5,-5)$, $(8,-8)$
Figure M vertices: $(0,1)$, $(0,5)$, $(-1,7)$

Step2: Reflect over x-axis

Flip L across x-axis: $(x,y)\to(x,-y)$
New points: $(5,1)$, $(5,5)$, $(8,8)$

Step3: Translate left 5 units

Shift left by 5: $(x,y)\to(x-5,y)$
New points: $(0,1)$, $(0,5)$, $(3,8)$

Step4: Reflect over y-axis

Flip across y-axis: $(x,y)\to(-x,y)$
New points: $(0,1)$, $(0,5)$, $(-3,8)$

Step5: Translate up 0, right 2

Shift right by 2: $(x,y)\to(x+2,y)$
Final points: $(0,1)$, $(0,5)$, $(-1,8)$ (matches M)

Answer:

1. Reflect Figure L across the x-axis.
2. Translate the resulting figure 5 units to the left.
3. Reflect the new figure across the y-axis.
4. Translate the final figure 2 units to the right.

Alternative valid sequence: Reflect over x-axis, translate left 5, reflect over y-axis, translate up 0/right 2 (or equivalent combined transformations that achieve the same mapping)