Question

determine the coordinates for each of the following * 12 point rotation 180° about the origin (2,-3) (-1,0) (-4,-2) (2,0) (-5,3) (0,-1) (0,-4) (-1,-4) (3,-4) (3 y j r

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) about the origin, the new coordinates \((x',y')\) are given by the rule \((x',y')=(-x,-y)\).

Step2: Find coordinates for \(V\)

Assume \(V=(2,0)\). Using the rule \((x',y') = (-x,-y)\), we substitute \(x = 2\) and \(y = 0\). Then \(x'=-2\) and \(y' = 0\).

Step3: Find coordinates for \(J\)

Assume \(J=(-1,0)\). Using the rule \((x',y')=(-x,-y)\), we substitute \(x=-1\) and \(y = 0\). Then \(x' = 1\) and \(y'=0\).

Step4: Find coordinates for \(R\)

Assume \(R=(2,-3)\). Using the rule \((x',y')=(-x,-y)\), we substitute \(x = 2\) and \(y=-3\). Then \(x'=-2\) and \(y' = 3\).

Answer:

If \(V=(2,0)\), \(V'\) is \((-2,0)\); if \(J=(-1,0)\), \(J'\) is \((1,0)\); if \(R=(2,-3)\), \(R'\) is \((-2,3)\)