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): $A_1=(-1,5)$
For point L(-3,-2): $L_1=(-2,3)$
For point T(-3,2): $T_1=(2,3)$

Step2: Apply x - axis reflection rule

The rule for reflecting a point over the x - axis is $(x,y)\to(x, - y)$.
For point $A_1(-1,5)$: $A_2=(-1,-5)$
For point $L_1(-2,3)$: $L_2=(-2,-3)$
For point $T_1(2,3)$: $T_2=(2,-3)$

for part e:

Step1: Apply 180 - degree clockwise rotation rule

The rule for a 180 - degree clockwise rotation around the origin is $(x,y)\to(-x,-y)$.
For point A(-5,-1): $A_1=(5,1)$
For point L(-3,-2): $L_1=(3,2)$
For point T(-3,2): $T_1=(3,-2)$

Step2: Apply y - axis reflection rule

The rule for reflecting a point over the y - axis is $(x,y)\to(-x,y)$.
For point $A_1(5,1)$: $A_2=(-5,1)$
For point $L_1(3,2)$: $L_2=(-3,2)$
For point $T_1(3,-2)$: $T_2=(-3,-2)$

Answer:

The new coordinates of $\triangle ALT$ are $A(-1,-5)$, $L(-2,-3)$, $T(2,-3)$