Answer:
C. (-2, 4)
Step-by-step explanation:
First we are going to rotate the point 270°; then we are going to shift it down 3 units.
Remember that the rule to rotate a point 270° counterclockwise about the origin is:
[tex]R_{270}(y,-x)[/tex]
In other words, we just need to switch the coordinates and change the sign of the second coordinate. Let's apply the rule to our point:
[tex]A = (-7, -2)[/tex]
[tex]A'=(y,-x)=(-2,--7)=(-2,7)[/tex]
Now we know that the coordinates of our point after the rotation are A' = (-2, 7)
The only thing left is shift that point 3 units down; to do it, we just need to subtract 3 from the y-coordinate:
[tex](x,y)-->(x,y-3)[/tex]
[tex]A'=(-2,7)[/tex]
[tex]K'=(-2,7-3)[/tex]
[tex]K'=(-2,4)[/tex]
We can conclude that after a rotation of 270° and a translation 3 units down, the coordinates of point K' are (-2, 4).
