Question

Point J located at (2, 7) is rotated 90 degrees counterclockwise about (-1, -3). What is the y-coordinate of J’?

A. 9
B. 0
C. -11
D. -9

Answer 1

Given:

Coordinates of point J are J(2,7).

It is rotated 90 degrees counterclockwise about (-1, -3).

To find:

The y-coordinate of J’.

Solution:

If a figure rotated 90 degrees counterclockwise about a point (a,b), then

`(x,y)\to (-(y-b)+a,(x-a)+b)`

Point J is rotated 90 degrees counterclockwise about (-1, -3). So, a=-1 and b=-3.

`(x,y)\to (-(y-(-3))+(-1),(x-(-1))+(-3))`

`(x,y)\to (-(y+3)-1,(x+1)-3)`

`(x,y)\to (-y-3-1,x+1-3)`

`(x,y)\to (-y-4,x-2)`

Coordinates of point J are J(2,7).

`J(2,7)\to J'(-7-4,2-2)`

`J(2,7)\to J'(-11,0)`

Therefore, the y-coordinate of J' is 0. Hence, the correct option is B.