Question

triangle jkl is transformed using the rule ( r_{o, 90^circ} circ r_{y = -x}(x, y) ). point k of the pre - image is at (4, 7). what are the coordinates of point k on the final image?
( circ (-7, -4) )
( circ (-4, -7) )
( circ (4, -7) )
( circ (4, 7) )

Explanation:

Step1: Apply reflection $r_{y=-x}$

The rule for reflection over $y=-x$ is $(x,y) \to (-y,-x)$.
For point $K(4,7)$:
$(-7, -4)$

Step2: Apply rotation $R_{O,90^\circ}$

The rule for 90° counterclockwise rotation about the origin is $(x,y) \to (-y,x)$.
For the point $(-7,-4)$:
$(-(-4), -7) = (4, -7)$

Answer:

(4, -7)