Question

1. a point at (4,7) is reflected across the line x = - 1, then translated by the vector (3,-2), and finally rotated 270° counterclockwise about the origin. what is the location of the final image?

. a) (-5,-6)
. b) (5,3)
. c) (-5,6)
. d) (-6,5)

Explanation:

Step1: Calculate reflection across x = - 1

The distance between x = 4 and x=-1 is $4-(-1)=5$. The new x - coordinate after reflection across x = - 1 is $-1 - 5=-6$. The y - coordinate remains the same. So the point after reflection is (-6,7).

Step2: Perform translation

Add the components of the vector (3,-2) to the coordinates of the reflected point. The new x - coordinate is $-6 + 3=-3$, and the new y - coordinate is $7+( - 2)=5$. So the point after translation is (-3,5).

Step3: Perform 270° counter - clockwise rotation about the origin

The rule for a 270° counter - clockwise rotation about the origin $(x,y)\to(y,-x)$. For the point (-3,5), the new x - coordinate is 5 and the new y - coordinate is 3. So the final point is (5,3).

Answer:

B. (5,3)