Question

1. what are the coordinates of b after the following composition of transformations

rotation 90° clockwise about the origin
translation (x,y)→(x + 2,y - 4)
a. (-2,-2)
b. (4,0)
c. (0,4)
d. (-4,3)

Explanation:

Step1: Determine the coordinates of point B

From the graph, the coordinates of point B are (-2, 2).

Step2: Apply the 90 - degree clock - wise rotation formula

The formula for a 90 - degree clock - wise rotation about the origin is $(x,y)\to(y, - x)$. For point B(-2, 2), after rotation, the new coordinates $B'$ are $(2,2)$.

Step3: Apply the translation

The translation rule is $(x,y)\to(x + 2,y - 4)$. For point $B'(2,2)$, we have $x=2$ and $y = 2$. After translation, $x'=2 + 2=4$ and $y'=2-4=-2$. So the coordinates of $B''$ are $(4,0)$.

Answer:

B. (4,0)