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QuestionFind the new coordinates of (−1,3)(-1,3) after moving 2 units down and rotating 270∘270^{\circ} counterclockwise around the origin.

Studdy Solution

STEP 1

Assumptions1. The initial point is (−1,3)(-1,3). The point is first translated units down3. After the translation, the point is rotated 270∘270^{\circ} counterclockwise about the origin

STEP 2

First, we perform the translation. A translation down by2 units subtracts2 from the y-coordinate of the point.
(−1,)→(−1,−2)(-1,) \rightarrow (-1,-2)

STEP 3

Calculate the new coordinates after the translation.
(−1,3−2)=(−1,1)(-1,3-2) = (-1,1)

STEP 4

Now we perform the rotation. A rotation of 270∘270^{\circ} counterclockwise about the origin is equivalent to a rotation of 90∘90^{\circ} clockwise. The formula for a 90∘90^{\circ} clockwise rotation is (x,y)→(y,−x)(x,y) \rightarrow (y,-x).
(−1,1)→(1,1)(-1,1) \rightarrow (1,1)

STEP 5

The image of (−1,3)(-1,3) obtained by translating2 units down, followed by a rotation of 270∘270^{\circ} counterclockwise about the origin is (1,1)(1,1).

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