Question

point d (7, 8) was rotated about the origin, creating point d (-8, 7). use the drop-down menus to describe the rotation that resulted in d. point d was rotated 90° about the origin. clockwise counter - clockwise

Explanation:

Step1: Recall Rotation Rules

For a point \((x, y)\) rotated about the origin:

• \(90^\circ\) clockwise: \((x, y) \to (y, -x)\)
• \(90^\circ\) counter - clockwise: \((x, y) \to (-y, x)\)
• \(180^\circ\) clockwise/counter - clockwise: \((x, y) \to (-x, -y)\)
• \(270^\circ\) clockwise: \((x, y) \to (-y, x)\) (same as \(90^\circ\) counter - clockwise)
• \(270^\circ\) counter - clockwise: \((x, y) \to (y, -x)\) (same as \(90^\circ\) clockwise)

Step2: Apply to Point \(D(7, 8)\)

We have \(D(7, 8)\) and \(D'(-8, 7)\).
Compare with the rotation rules. If we use the \(90^\circ\) counter - clockwise rule \((x, y)\to(-y, x)\), substituting \(x = 7\) and \(y = 8\), we get \((-8, 7)\), which matches the coordinates of \(D'\).
If we use the \(90^\circ\) clockwise rule \((x, y)\to(y, -x)\), substituting \(x = 7\) and \(y = 8\), we get \((8, -7)\), which does not match \(D'(-8, 7)\).

Answer:

counter - clockwise