Question

you do: check for understanding
point q with coordinates (4, -7) is rotated to q(7, 4). describe the rotation that maps q onto q and represent it algebraically.

Explanation:

Step1: Recall rotation rules

For a \(90^{\circ}\) counter - clockwise rotation about the origin, the rule is \((x,y)\to(-y,x)\)

Step2: Apply the rule

Given \(Q(4,-7)\), when we apply the rule \((x,y)\to(-y,x)\), we substitute \(x = 4\) and \(y=-7\). Then \(-y=-(-7) = 7\) and \(x = 4\). So the image is \((7,4)\) which is \(Q'\)

Answer:

The rotation is a \(90^{\circ}\) counter - clockwise rotation about the origin. The algebraic representation is \((x,y)\to(-y,x)\)