Question

consider △abc with a (-4, 2), b (-4, -1), and c (-2, -1) plotted on the grid below. perform the following sequence of transformations and then give the coordinates of a, b, and c. translate △abc 5 units right and 2 units up. then, rotate it 90° clockwise about the origin. note: do not use any spaces in your answer. the coordinates of a are the coordinates of b are the coordinates of c are

Explanation:

Step1: Perform translation

For a point $(x,y)$ translated $a = 5$ units right and $b=2$ units up, the new - point $(x',y')$ is given by $(x + a,y + b)$.
For $A(-4,2)$: $x=-4,y = 2$, then $x'=-4 + 5=1,y'=2 + 2 = 4$, so $A_1=(1,4)$.
For $B(-4,-1)$: $x=-4,y=-1$, then $x'=-4 + 5 = 1,y'=-1+2 = 1$, so $B_1=(1,1)$.
For $C(-2,-1)$: $x=-2,y=-1$, then $x'=-2 + 5 = 3,y'=-1 + 2=1$, so $C_1=(3,1)$.

Step2: Perform 90 - degree clock - wise rotation about the origin

The rule for a 90 - degree clock - wise rotation about the origin for a point $(x,y)$ is $(y,-x)$.
For $A_1(1,4)$: $x = 1,y = 4$, then $A'=(4,-1)$.
For $B_1(1,1)$: $x = 1,y = 1$, then $B'=(1,-1)$.
For $C_1(3,1)$: $x = 3,y = 1$, then $C'=(1,-3)$.

Answer:

The coordinates of $A'$ are $(4,-1)$
The coordinates of $B'$ are $(1,-1)$
The coordinates of $C'$ are $(1,-3)$