QuestionReflect point $C(-1,-6)$ across the line $y=4$ . What are the coordinates of $C^{\prime}$ ?

Studdy Solution

STEP 1

Assumptions1. The polygon ABC has vertices A(-4,-4), B(-4,-6), C(-1,-6), D(-1,-4). . The reflection is across the line y=4.
3. We need to find the image coordinates of C' after the reflection.

STEP 2

The rule for reflecting a point across a horizontal line y = k is (x, y) -> (x,2k - y). Here, k is the y-coordinate of the line of reflection.

STEP 3

Let's apply this rule to point C(-1,-6) to find the coordinates of C'. $C' = (-1,2* - (-6))$

STEP 4

Now, calculate the y-coordinate of C'.
$C' = (-1,8 - (-6))$

STEP 5

implify the y-coordinate of C'.
$C' = (-1,8 +)$

STEP 6

Calculate the final coordinates of C'.
$C' = (-1,14)$ So, the image coordinates of C' after the reflection across y=4 are (-1,14).

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QuestionReflect point $C(-1,-6)$ across the line $y=4$ . What are the coordinates of $C^{\prime}$ ?

Studdy Solution

STEP 1

Assumptions1. The polygon ABC has vertices A(-4,-4), B(-4,-6), C(-1,-6), D(-1,-4). . The reflection is across the line y=4.
3. We need to find the image coordinates of C' after the reflection.

STEP 2

The rule for reflecting a point across a horizontal line y = k is (x, y) -> (x,2k - y). Here, k is the y-coordinate of the line of reflection.

STEP 3

Let's apply this rule to point C(-1,-6) to find the coordinates of C'. $C' = (-1,2* - (-6))$

STEP 4

Now, calculate the y-coordinate of C'.
$C' = (-1,8 - (-6))$

STEP 5

implify the y-coordinate of C'.
$C' = (-1,8 +)$

STEP 6

Calculate the final coordinates of C'.
$C' = (-1,14)$ So, the image coordinates of C' after the reflection across y=4 are (-1,14).

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QuestionReflect point C(−1,−6)C(-1,-6)C(−1,−6) across the line y=4y=4y=4. What are the coordinates of C′C^{\prime}C′?

Studdy Solution

STEP 1

Assumptions1. The polygon ABC has vertices A(-4,-4), B(-4,-6), C(-1,-6), D(-1,-4). . The reflection is across the line y=4.3. We need to find the image coordinates of C' after the reflection.

STEP 2

The rule for reflecting a point across a horizontal line y = k is (x, y) -> (x,2k - y). Here, k is the y-coordinate of the line of reflection.

STEP 3

Let's apply this rule to point C(-1,-6) to find the coordinates of C'.C′=(−1,2∗−(−6))C' = (-1,2* - (-6))C′=(−1,2∗−(−6))

STEP 4

Now, calculate the y-coordinate of C'.C′=(−1,8−(−6))C' = (-1,8 - (-6))C′=(−1,8−(−6))

STEP 5

implify the y-coordinate of C'.C′=(−1,8+)C' = (-1,8 +)C′=(−1,8+)

STEP 6

Calculate the final coordinates of C'.C′=(−1,14)C' = (-1,14)C′=(−1,14)So, the image coordinates of C' after the reflection across y=4 are (-1,14).

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QuestionReflect point $C(-1,-6)$ across the line $y=4$ . What are the coordinates of $C^{\prime}$ ?

Assumptions1. The polygon ABC has vertices A(-4,-4), B(-4,-6), C(-1,-6), D(-1,-4). . The reflection is across the line y=4.
3. We need to find the image coordinates of C' after the reflection.

Let's apply this rule to point C(-1,-6) to find the coordinates of C'. $C' = (-1,2* - (-6))$

Now, calculate the y-coordinate of C'.
$C' = (-1,8 - (-6))$

implify the y-coordinate of C'.
$C' = (-1,8 +)$

Calculate the final coordinates of C'.
$C' = (-1,14)$ So, the image coordinates of C' after the reflection across y=4 are (-1,14).