Question

1. a point s is at (-1,-4). it is reflected across the line x = 2, rotated 90 degrees counterclockwise about the origin, and then translated by (x,y)→(x,y + 5). find the coordinates of the final image of s.

. a) (9,0)
. b) (4,10)
. c) (-9,6)
. d) (4,0)

Explanation:

Step1: Find the reflection across x = 2

The distance between x=-1 and x = 2 is $2-(-1)=3$. The x - coordinate of the reflected point will be $2 + 3=5$, and the y - coordinate remains the same. So the point after reflection across x = 2 is $(5,-4)$.

Step2: Perform 90 - degree counter - clockwise rotation about the origin

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$. For the point $(5,-4)$, after rotation, it becomes $(4,5)$.

Step3: Apply the translation

The translation rule is $(x,y)\to(x,y + 5)$. For the point $(4,5)$, after translation, we have $(4,5+5)=(4,10)$.

Answer:

B. (4,10)