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? (-7, -4) (-4, -7) (4, -7) (4, 7)

Explanation:

Step1: Apply reflection rule

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: Apply rotation rule

The rule $R_{0,90^{\circ}}(x,y)=(-y,x)$. Applying this to the point $(-7,-4)$ gives $-(-4),-7=(4, - 7)$.

Answer:

$(4,-7)$