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
[tex](x,y)\to (-(y-b)+a,(x-a)+b)[/tex]
Point J is rotated 90 degrees counterclockwise about (-1, -3). So, a=-1 and b=-3.
[tex](x,y)\to (-(y-(-3))+(-1),(x-(-1))+(-3))[/tex]
[tex](x,y)\to (-(y+3)-1,(x+1)-3)[/tex]
[tex](x,y)\to (-y-3-1,x+1-3)[/tex]
[tex](x,y)\to (-y-4,x-2)[/tex]
Coordinates of point J are J(2,7).
[tex]J(2,7)\to J'(-7-4,2-2)[/tex]
[tex]J(2,7)\to J'(-11,0)[/tex]
Therefore, the y-coordinate of J' is 0. Hence, the correct option is B.
