Question

a point at (6,-4) is translated by the vector (-2,3), then reflected across the x - axis, and finally rotated 270° counterclockwise about the origin. what is the location of the final image?
. a) (-7,4)
. b) (1,4)
. c) (-4,-1)
. d) (1,-4)
○ a) (-7,4)
○ b) (1,4)
● c) (-4,-1)
○ d) (1,-4)

Explanation:

Step1: Perform translation

Add the components of the vector to the coordinates of the point. Given point $(6,-4)$ and vector $\langle - 2,3
angle$. The new - point after translation is $(6+( - 2),-4 + 3)=(4,-1)$.

Step2: Perform reflection across the x - axis

When a point $(x,y)$ is reflected across the x - axis, the x - coordinate remains the same and the y - coordinate changes its sign. So, for the point $(4,-1)$, after reflection across the x - axis, it becomes $(4,1)$.

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

The rule for a 270 - degree counter - clockwise rotation about the origin is $(x,y)\to(y,-x)$. For the point $(4,1)$, after rotation, it becomes $(1,-4)$.

Answer:

D. $(1,-4)$