Question

polygon abcd is defined by the points a(-5, 1), b(-4, 3), c(-2, 7) and d(-1, 2). if the polygon rotates 90° counterclockwise to create polygon abcd, what are the coordinates of c? (-2, -7) (-7, -2) (7, 2) (2, -7)

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) are given by the rule \((x,y)\to(-y,x)\).

Step2: Apply the rule to point \(C(-2,7)\)

For point \(C\) with \(x=-2\) and \(y = 7\), using the formula \((x,y)\to(-y,x)\), we substitute \(x=-2\) and \(y = 7\) into the formula.
First, find \(-y\): \(-y=-7\).
Second, find \(x\): \(x=-2\).
The new coordinates \((x',y')\) are \((-7,-2)\).

Answer:

\((-7,-2)\) (the second option)