Question

c) rotate △alt if a(-5,-1), l(-3,-2), t(-3,2) 90° clockwise around the origin, then reflect the image over the x - axis.
e) rotate △alt if a(-5,-1), l(-3,-2), t(-3,2) 180° clockwise around the origin, then reflect the image over the y - axis.

Explanation:

Step1: Apply 90 - degree clockwise rotation rule

The rule for a 90 - degree clockwise rotation around the origin is $(x,y)\to(y, - x)$.
For point A(-5,-1), after rotation: $A'=(-1,5)$; for L(-3,-2), $L'=(-2,3)$; for T(-3,2), $T'=(2,3)$.

Step2: Apply x - axis reflection rule

The rule for reflecting a point $(x,y)$ over the x - axis is $(x,y)\to(x, - y)$.
For $A'(-1,5)$, after reflection $A''=(-1,-5)$; for $L'(-2,3)$, $L''=(-2,-3)$; for $T'(2,3)$, $T''=(2,-3)$.

Step3: Apply 180 - degree clockwise rotation rule (for part e)

The rule for a 180 - degree clockwise rotation around the origin is $(x,y)\to(-x,-y)$.
For point A(-5,-1), after rotation: $A'=(5,1)$; for L(-3,-2), $L'=(3,2)$; for T(-3,2), $T'=(3,-2)$.

Step4: Apply y - axis reflection rule (for part e)

The rule for reflecting a point $(x,y)$ over the y - axis is $(x,y)\to(-x,y)$.
For $A'(5,1)$, after reflection $A''=(-5,1)$; for $L'(3,2)$, $L''=(-3,2)$; for $T'(3,-2)$, $T''=(-3,-2)$.

Answer:

c) The new coordinates of the vertices of the triangle after the transformation are A''(-1,-5), L''(-2,-3), T''(2,-3).
e) The new coordinates of the vertices of the triangle after the transformation are A''(-5,1), L''(-3,2), T''(-3,-2).