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A triangle has vertices W(−3,7) ,Q(1,−1) , and Z(−5,−2) . Apply rotation mapping rules to find the coordinates of W′ after a 90-degree (counterclockwise) rotation about the origin

W′ (Answer,here)

1 answer

To rotate a point \( (x, y) \) by 90 degrees counterclockwise about the origin, the formula used is:

\[ (x, y) \rightarrow (-y, x) \]

Given the vertex \( W(-3, 7) \):

  1. Identify \( x \) and \( y \):

    • \( x = -3 \)
    • \( y = 7 \)

  2. Apply the rotation formula:

    • New \( x \) = \( -y = -7 \)
    • New \( y \) = \( x = -3 \)

Thus, the coordinates of \( W' \) after the rotation are:

\[ W' = (-7, -3) \]

So, the answer is:

\[ W' = (-7, -3) \]