Question

triangle jkl has vertices j(2,5), k(4,2), and l(1,1). it is rotated 270 degrees counterclockwise about the origin, translated by (x,y)→(x + 2,y - 3), and then reflected across the line y = x. what are the coordinates of vertex k?
. a) (-7,4)
. b) (4,-7)
. c) (-1,0)
. d) (0,-1)
o a) (-7,4)
o b) (4,-7)
o c) (-1,0)
o d) (0,-1)

Explanation:

Step1: Apply 270 - degree counter - clockwise rotation

The rule for a 270 - degree counter - clockwise rotation about the origin is $(x,y)\to(y, - x)$. For point $K(4,2)$, after rotation, we get $K_1(2,-4)$.

Step2: Apply translation

The translation rule is $(x,y)\to(x + 2,y-3)$. For $K_1(2,-4)$, we have $x=2$ and $y = - 4$. Then $x+2=2 + 2=4$ and $y-3=-4-3=-7$. So the new point $K_2(4,-7)$.

Step3: Apply reflection across the line $y = x$

The rule for reflection across the line $y = x$ is $(x,y)\to(y,x)$. For $K_2(4,-7)$, after reflection, we get $K_3(-7,4)$.

Answer:

A. (-7,4)