Question

triangle jkl is transformed using the rule $r_{0,90^{circ}}circ r_{y = - x}(x,y)$. point k of the pre - image is at $(4,7)$. what are the coordinates of point k on the final image? (-4,-7) (-7,-4) (4,-7) (4,7)

Explanation:

Step1: Perform reflection

The rule $r_{y = -x}(x,y)$ swaps the $x$ and $y$ - coordinates and changes their signs. For point $K(4,7)$, applying $r_{y=-x}(x,y)$ gives $(-7,-4)$.

Step2: Perform rotation

The rule $R_{0,90^{\circ}}$ rotates a point $(x,y)$ counter - clockwise about the origin by $90^{\circ}$. The transformation rule for a $90^{\circ}$ counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$. For the point $(-7,-4)$ after reflection, applying $R_{0,90^{\circ}}$ gives $-(-4),-7=(4, - 7)$.

Answer:

$(4,-7)$