Math / Geometry

QuestionThe point $W(5,-2)$ is reflected over the $y$ -axis. What are the coordinates of the resulting point, W'? $W^{\prime}($ $\square$ , $\square$

Studdy Solution

STEP 1

1. The point $W(5, -2)$ is given in the Cartesian coordinate system.
2. The reflection is over the $y$ -axis.

STEP 2

1. Understand the reflection over the $y$ -axis.
2. Apply the reflection to the point $W$ .
3. Determine the coordinates of the reflected point $W'$ .

STEP 3

Understand the reflection over the $y$ -axis:
- Reflecting a point over the $y$ -axis changes the sign of the $x$ -coordinate, while the $y$ -coordinate remains unchanged.

STEP 4

Apply the reflection to the point $W(5, -2)$ :
- Change the sign of the $x$ -coordinate: $5 \rightarrow -5$ . - Keep the $y$ -coordinate the same: $-2$ .

STEP 5

Determine the coordinates of the reflected point $W'$ :
- The coordinates of $W'$ are $(-5, -2)$ .
The coordinates of the reflected point $W'$ are:
$W'(-5, -2)$

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QuestionThe point $W(5,-2)$ is reflected over the $y$ -axis. What are the coordinates of the resulting point, W'? $W^{\prime}($ $\square$ , $\square$

Studdy Solution

STEP 1

1. The point $W(5, -2)$ is given in the Cartesian coordinate system.
2. The reflection is over the $y$ -axis.

STEP 2

1. Understand the reflection over the $y$ -axis.
2. Apply the reflection to the point $W$ .
3. Determine the coordinates of the reflected point $W'$ .

STEP 3

Understand the reflection over the $y$ -axis:
- Reflecting a point over the $y$ -axis changes the sign of the $x$ -coordinate, while the $y$ -coordinate remains unchanged.

STEP 4

Apply the reflection to the point $W(5, -2)$ :
- Change the sign of the $x$ -coordinate: $5 \rightarrow -5$ . - Keep the $y$ -coordinate the same: $-2$ .

STEP 5

Determine the coordinates of the reflected point $W'$ :
- The coordinates of $W'$ are $(-5, -2)$ .
The coordinates of the reflected point $W'$ are:
$W'(-5, -2)$

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QuestionThe point W(5,−2)W(5,-2)W(5,−2) is reflected over the yyy-axis. What are the coordinates of the resulting point, W'? W′(W^{\prime}(W′( □\square□ , □\square□

Studdy Solution

STEP 1

1. The point W(5,−2) W(5, -2) W(5,−2) is given in the Cartesian coordinate system.2. The reflection is over the y y y-axis.

STEP 2

1. Understand the reflection over the y y y-axis.2. Apply the reflection to the point W W W.3. Determine the coordinates of the reflected point W′ W' W′.

STEP 3

Understand the reflection over the y y y-axis:- Reflecting a point over the y y y-axis changes the sign of the x x x-coordinate, while the y y y-coordinate remains unchanged.

STEP 4

Apply the reflection to the point W(5,−2) W(5, -2) W(5,−2):- Change the sign of the x x x-coordinate: 5→−5 5 \rightarrow -5 5→−5. - Keep the y y y-coordinate the same: −2-2−2.

STEP 5

Determine the coordinates of the reflected point W′ W' W′:- The coordinates of W′ W' W′ are (−5,−2)(-5, -2)(−5,−2). The coordinates of the reflected point W′ W' W′ are:W′(−5,−2) W'(-5, -2) W′(−5,−2)

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QuestionThe point $W(5,-2)$ is reflected over the $y$ -axis. What are the coordinates of the resulting point, W'? $W^{\prime}($ $\square$ , $\square$

1. The point $W(5, -2)$ is given in the Cartesian coordinate system.
2. The reflection is over the $y$ -axis.

1. Understand the reflection over the $y$ -axis.
2. Apply the reflection to the point $W$ .
3. Determine the coordinates of the reflected point $W'$ .

Understand the reflection over the $y$ -axis:
- Reflecting a point over the $y$ -axis changes the sign of the $x$ -coordinate, while the $y$ -coordinate remains unchanged.

Apply the reflection to the point $W(5, -2)$ :
- Change the sign of the $x$ -coordinate: $5 \rightarrow -5$ . - Keep the $y$ -coordinate the same: $-2$ .

Determine the coordinates of the reflected point $W'$ :
- The coordinates of $W'$ are $(-5, -2)$ .
The coordinates of the reflected point $W'$ are:
$W'(-5, -2)$