Question

graph the image of \\( \triangle k l m \\) after a rotation \\( 270^{\circ} \\) clockwise around the origin.

Explanation:

Step1: Recall the rotation rule

The rule for a \(270^{\circ}\) clockwise rotation around the origin is \((x,y)\to(y, -x)\).

Step2: Find the coordinates of the original points

Assume \(K(-1,-9)\), \(L(-1,-6)\), \(M(0,-6)\) (by observing the graph).

Step3: Apply the rotation rule

For point \(K(-1,-9)\):
Substitute \(x = - 1\), \(y=-9\) into \((x,y)\to(y, -x)\), we get \(K'(-9,1)\).
For point \(L(-1,-6)\):
Substitute \(x=-1\), \(y = - 6\) into \((x,y)\to(y, -x)\), we get \(L'(-6,1)\).
For point \(M(0,-6)\):
Substitute \(x = 0\), \(y=-6\) into \((x,y)\to(y, -x)\), we get \(M'(-6,0)\).

Step4: Plot the new points

Plot \(K'(-9,1)\), \(L'(-6,1)\), \(M'(-6,0)\) on the coordinate plane and connect them to form \(\triangle K'L'M'\).

Answer:

Plot the points \(K'(-9,1)\), \(L'(-6,1)\), \(M'(-6,0)\) and connect them.