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 about the origin. 90° 180° 270° 360°

Explanation:

Step1: Recall rotation rules

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

• \(90^\circ\) counterclockwise: \((-y, x)\)
• \(90^\circ\) clockwise (or \(270^\circ\) counterclockwise): \((y, -x)\)
• \(180^\circ\): \((-x, -y)\)
• \(270^\circ\) clockwise (or \(90^\circ\) counterclockwise): \((-y, x)\) Wait, correction: \(90^\circ\) counterclockwise: \((-y, x)\); \(270^\circ\) counterclockwise (or \(90^\circ\) clockwise): \((y, -x)\)

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

Let's check each rotation:

• \(90^\circ\) counterclockwise: \((-8, 7)\) (since \(x = 7\), \(y = 8\), so \(-y=-8\), \(x = 7\))
• \(180^\circ\): \((-7, -8)\) (not matching \(D'(-8,7)\))
• \(270^\circ\) counterclockwise: \((8, -7)\) (not matching)
• \(360^\circ\): \((7, 8)\) (same as original, not matching)

So the rotation is \(90^\circ\) counterclockwise (or \(270^\circ\) clockwise, but the drop - down has \(90^\circ\) as an option which matches the result \((-8,7)\) when we do \(90^\circ\) counterclockwise rotation on \((7,8)\)).

Answer:

\(90^\circ\)