QuestionFind the new coordinates of the point $(2,-6)$ after applying the transformations $R_{270^{\circ}}$ and then $r_{\mathrm{y} \text{-axis}}$ .

Studdy Solution

STEP 1

Assumptions1. The original point is $(,-6)$ . The transformation is a rotation of $270^{\circ}$ followed by a reflection in the y-axis3. The rotation is counterclockwise4. The rotation is about the origin

STEP 2

First, we need to perform the rotation of $270^{\circ}$ . The formula for a rotation of $270^{\circ}$ about the origin is $(x,y) \rightarrow (-y,x)$ .

STEP 3

Now, plug in the given values for $x$ and $y$ to perform the rotation.
$(2,-6) \rightarrow (-(-6),2)$

STEP 4

Calculate the new coordinates after the rotation.
$(2,-6) \rightarrow (6,2)$

STEP 5

Next, we need to perform the reflection in the y-axis. The formula for a reflection in the y-axis is $(x,y) \rightarrow (-x,y)$ .

STEP 6

Now, plug in the new coordinates for $x$ and $y$ to perform the reflection.
$(6,2) \rightarrow (-6,2)$ The image point of $(2,-6)$ after the transformation $R_{270^{\circ}} \circ r_{\mathrm{y} \text {-axis? }}$ is $(-6,2)$ .

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QuestionFind the new coordinates of the point $(2,-6)$ after applying the transformations $R_{270^{\circ}}$ and then $r_{\mathrm{y} \text{-axis}}$ .

Studdy Solution

STEP 1

Assumptions1. The original point is $(,-6)$ . The transformation is a rotation of $270^{\circ}$ followed by a reflection in the y-axis3. The rotation is counterclockwise4. The rotation is about the origin

STEP 2

First, we need to perform the rotation of $270^{\circ}$ . The formula for a rotation of $270^{\circ}$ about the origin is $(x,y) \rightarrow (-y,x)$ .

STEP 3

Now, plug in the given values for $x$ and $y$ to perform the rotation.
$(2,-6) \rightarrow (-(-6),2)$

STEP 4

Calculate the new coordinates after the rotation.
$(2,-6) \rightarrow (6,2)$

STEP 5

Next, we need to perform the reflection in the y-axis. The formula for a reflection in the y-axis is $(x,y) \rightarrow (-x,y)$ .

STEP 6

Now, plug in the new coordinates for $x$ and $y$ to perform the reflection.
$(6,2) \rightarrow (-6,2)$ The image point of $(2,-6)$ after the transformation $R_{270^{\circ}} \circ r_{\mathrm{y} \text {-axis? }}$ is $(-6,2)$ .

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QuestionFind the new coordinates of the point (2,−6)(2,-6)(2,−6) after applying the transformations R270∘R_{270^{\circ}}R270∘​ and then ry-axisr_{\mathrm{y} \text{-axis}}ry-axis​.

Studdy Solution

STEP 1

Assumptions1. The original point is (,−6)(,-6)(,−6). The transformation is a rotation of 270∘270^{\circ}270∘ followed by a reflection in the y-axis3. The rotation is counterclockwise4. The rotation is about the origin

STEP 2

First, we need to perform the rotation of 270∘270^{\circ}270∘. The formula for a rotation of 270∘270^{\circ}270∘ about the origin is (x,y)→(−y,x)(x,y) \rightarrow (-y,x)(x,y)→(−y,x).

STEP 3

Now, plug in the given values for xxx and yyy to perform the rotation.(2,−6)→(−(−6),2)(2,-6) \rightarrow (-(-6),2)(2,−6)→(−(−6),2)

STEP 4

Calculate the new coordinates after the rotation.(2,−6)→(6,2)(2,-6) \rightarrow (6,2)(2,−6)→(6,2)

STEP 5

Next, we need to perform the reflection in the y-axis. The formula for a reflection in the y-axis is (x,y)→(−x,y)(x,y) \rightarrow (-x,y)(x,y)→(−x,y).

STEP 6

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QuestionFind the new coordinates of the point $(2,-6)$ after applying the transformations $R_{270^{\circ}}$ and then $r_{\mathrm{y} \text{-axis}}$ .

Assumptions1. The original point is $(,-6)$ . The transformation is a rotation of $270^{\circ}$ followed by a reflection in the y-axis3. The rotation is counterclockwise4. The rotation is about the origin

First, we need to perform the rotation of $270^{\circ}$ . The formula for a rotation of $270^{\circ}$ about the origin is $(x,y) \rightarrow (-y,x)$ .

Now, plug in the given values for $x$ and $y$ to perform the rotation.
$(2,-6) \rightarrow (-(-6),2)$

Calculate the new coordinates after the rotation.
$(2,-6) \rightarrow (6,2)$

Next, we need to perform the reflection in the y-axis. The formula for a reflection in the y-axis is $(x,y) \rightarrow (-x,y)$ .