Question

graph the image of \\( \triangle jkl \\) after a rotation \\( 90 ^ { \circ } \\) counterclockwise around the origin and a translation 5 units down.

Explanation:

Step1: Find coordinates of original points

From the graph, \(J(4,5)\), \(K(5,1)\), \(L(1,1)\)

Step2: Apply \(90^{\circ}\) counter - clockwise rotation formula \((x,y)\to(-y,x)\)

For \(J(4,5)\): \((-5,4)\)
For \(K(5,1)\): \((-1,5)\)
For \(L(1,1)\): \((-1,1)\)

Step3: Apply translation 5 units down \((x,y)\to(x,y - 5)\)

For \(J'\) (after rotation): \((-5,4)\to(-5,4 - 5)=(-5,-1)\)
For \(K'\) (after rotation): \((-1,5)\to(-1,5 - 5)=(-1,0)\)
For \(L'\) (after rotation): \((-1,1)\to(-1,1 - 5)=(-1,-4)\)

Step4: Plot the new points \((-5,-1)\), \((-1,0)\), \((-1,-4)\) and connect them to form \(\triangle J'K'L'\)

Answer:

Plot the points \(J'(-5,-1)\), \(K'(-1,0)\), \(L'(-1,-4)\) and connect them.