Question

trapezoid g h j k was rotated 180° about the origin to determine the location of ghjk, as shown on the graph. what are the coordinates of pre - image point h? (2, 3) (-2, 3) (3, 2) (3, -2)

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) about the origin, the transformation rule is \((x,y)\to(-x,-y)\). Let the coordinates of the pre - image point \(H\) be \((a,b)\) and the coordinates of the image point \(H'\) be \((x,y)\). Then \(x=-a\) and \(y = -b\), or \(a=-x\) and \(b=-y\).

Step2: Identify the coordinates of \(H'\)

From the graph, the coordinates of \(H'\) are \((-2,-3)\).

Step3: Apply the reverse of the rotation rule

Using \(a=-x\) and \(b = -y\) with \(x=-2\) and \(y=-3\). Then \(a=-(-2)=2\) and \(b=-(-3)=3\).

Answer:

\((2,3)\) (the first option)