Question

Point A(-7, -2) is rotated 270° counterclockwise and then shifted down 3 units. What are to coordinates of K’?

A. (2,4)

B. (-2, -7)

C. (-2, 4)

D. (7, -5)

Answer 1

C. (-2, 4)

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:

`R_(270)(y,-x)`

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:

`A = (-7, -2)`

`A'=(y,-x)=(-2,--7)=(-2,7)`

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:

`(x,y)-->(x,y-3)`

`A'=(-2,7)`

`K'=(-2,7-3)`

`K'=(-2,4)`

We can conclude that after a rotation of 270° and a translation 3 units down, the coordinates of point K' are (-2, 4).