Point

Question

\[P\] was rotated by
\[90^\circ\] clockwise about the center of rotation shown.
6 solid points. Point A is the bottom right hand point. Point B is above point A. Point P is the highest point. Point D is the bottom left hand point. Point C is above point D. A solid point labeled center is in the middle of the page.
\[P\]
\[A\]
\[B\]
\[C\]
\[D\]
Which point is the image of
\[P\]?
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[A\]
A
\[A\]
(Choice B)
\[B\]
B
\[B\]
(Choice C)
\[C\]
C
\[C\]
(Choice D)
\[D\]
D
\[D\]

Answer 1

To determine the image of point \(P\) after a \(90^\circ\) clockwise rotation about the center, we first need to establish the relative positions of the points:

• Let the center be at the origin \((0,0)\).
• The points' coordinates might be loosely represented as follows, assuming the following arrangement:
  • Point \(A\): (1, -1)
  • Point \(B\): (1, 0)
  • Point \(P\): (0, 1)
  • Point \(D\): (-1, -1)
  • Point \(C\): (-1, 0)

When \(P(0, 1)\) undergoes a \(90^\circ\) clockwise rotation, we use the transformation rule: \[ (x,y) \to (y,-x) \] Applying this to point \(P(0, 1)\): \[ P(0, 1) \to (1, 0) \]

Now we identify the coordinates:

• Point \(B\) is at (1, 0), which matches the image of \(P\).

Thus, the image of point \(P\) after a \(90^\circ\) clockwise rotation about the center is point \(B\).

The correct answer is: (Choice B) \(B\)