Question

1. question 1 part 1: quadrilateral klmn has vertices k(2, 0), l(4, 0), m(5, -2), and n(1, -2). graph the figure and its rotated image after a counterclockwise rotation of 90° about the origin.

Explanation:

Step1: Recall rotation rule

The rule for a counterclockwise rotation of \(90^\circ\) about the origin is \((x,y)\to(-y,x)\).

Step2: Rotate point K(2, 0)

Using the rule, \(x = 2\), \(y = 0\). So the new point \(K'\) is \((-0,2)=(0,2)\).

Step3: Rotate point L(4, 0)

For \(L(4,0)\), \(x = 4\), \(y = 0\). The new point \(L'\) is \((-0,4)=(0,4)\).

Step4: Rotate point M(5, -2)

Using the rule, \(x = 5\), \(y = -2\). So the new point \(M'\) is \((-(-2),5)=(2,5)\).

Step5: Rotate point N(1, -2)

For \(N(1,-2)\), \(x = 1\), \(y = -2\). The new point \(N'\) is \((-(-2),1)=(2,1)\).

Answer:

The rotated vertices are \(K'(0, 2)\), \(L'(0, 4)\), \(M'(2, 5)\), and \(N'(2, 1)\). To graph, plot the original quadrilateral with \(K(2,0)\), \(L(4,0)\), \(M(5,-2)\), \(N(1,-2)\) and the rotated quadrilateral with the new vertices.