QuestionTranslate $(x, y) \rightarrow(x-4, y+1)$ and reflect the result across the line $y=1$ .

Studdy Solution

STEP 1

Assumptions1. We are given a transformation of a point $(x, y)$ to $(x-4, y+1)$ . . We are asked to reflect the transformed point across the line $y=1$ .

STEP 2

First, let's translate the point $(x, y)$ to $(x-4, y+1)$ .
$Translated\, point = (x-4, y+1)$

STEP 3

Now, we need to reflect this translated point across the line $y=1$ .
The reflection of a point $(x, y)$ across the line $y=k$ is given by $(x,2k-y)$ .

STEP 4

Substitute $k=1$ and the translated point $(x-4, y+1)$ into the reflection formula.
$Reflected\, point = (x-4,2*1 - (y+1))$

STEP 5

implify the expression for the reflected point.
$Reflected\, point = (x-4,2 - y -1)$

STEP 6

Further simplify the expression for the reflected point.
$Reflected\, point = (x-4,1 - y)$ So, the point $(x, y)$ after being translated to $(x-4, y+1)$ and then reflected across the line $y=1$ ends up at $(x-4,1 - y)$ .

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QuestionTranslate $(x, y) \rightarrow(x-4, y+1)$ and reflect the result across the line $y=1$ .

Studdy Solution

STEP 1

Assumptions1. We are given a transformation of a point $(x, y)$ to $(x-4, y+1)$ . . We are asked to reflect the transformed point across the line $y=1$ .

STEP 2

First, let's translate the point $(x, y)$ to $(x-4, y+1)$ .
$Translated\, point = (x-4, y+1)$

STEP 3

Now, we need to reflect this translated point across the line $y=1$ .
The reflection of a point $(x, y)$ across the line $y=k$ is given by $(x,2k-y)$ .

STEP 4

Substitute $k=1$ and the translated point $(x-4, y+1)$ into the reflection formula.
$Reflected\, point = (x-4,2*1 - (y+1))$

STEP 5

implify the expression for the reflected point.
$Reflected\, point = (x-4,2 - y -1)$

STEP 6

Further simplify the expression for the reflected point.
$Reflected\, point = (x-4,1 - y)$ So, the point $(x, y)$ after being translated to $(x-4, y+1)$ and then reflected across the line $y=1$ ends up at $(x-4,1 - y)$ .

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QuestionTranslate (x,y)→(x−4,y+1)(x, y) \rightarrow(x-4, y+1)(x,y)→(x−4,y+1) and reflect the result across the line y=1y=1y=1.

Studdy Solution

STEP 1

Assumptions1. We are given a transformation of a point (x,y)(x, y)(x,y) to (x−4,y+1)(x-4, y+1)(x−4,y+1). . We are asked to reflect the transformed point across the line y=1y=1y=1.

STEP 2

First, let's translate the point (x,y)(x, y)(x,y) to (x−4,y+1)(x-4, y+1)(x−4,y+1).Translated point=(x−4,y+1)Translated\, point = (x-4, y+1)Translatedpoint=(x−4,y+1)

STEP 3

Now, we need to reflect this translated point across the line y=1y=1y=1.The reflection of a point (x,y)(x, y)(x,y) across the line y=ky=ky=k is given by (x,2k−y)(x,2k-y)(x,2k−y).

STEP 4

Substitute k=1k=1k=1 and the translated point (x−4,y+1)(x-4, y+1)(x−4,y+1) into the reflection formula.Reflected point=(x−4,2∗1−(y+1))Reflected\, point = (x-4,2*1 - (y+1))Reflectedpoint=(x−4,2∗1−(y+1))

STEP 5

implify the expression for the reflected point.Reflected point=(x−4,2−y−1)Reflected\, point = (x-4,2 - y -1)Reflectedpoint=(x−4,2−y−1)

STEP 6

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QuestionTranslate $(x, y) \rightarrow(x-4, y+1)$ and reflect the result across the line $y=1$ .

Assumptions1. We are given a transformation of a point $(x, y)$ to $(x-4, y+1)$ . . We are asked to reflect the transformed point across the line $y=1$ .

First, let's translate the point $(x, y)$ to $(x-4, y+1)$ .
$Translated\, point = (x-4, y+1)$

Now, we need to reflect this translated point across the line $y=1$ .
The reflection of a point $(x, y)$ across the line $y=k$ is given by $(x,2k-y)$ .

Substitute $k=1$ and the translated point $(x-4, y+1)$ into the reflection formula.
$Reflected\, point = (x-4,2*1 - (y+1))$

implify the expression for the reflected point.
$Reflected\, point = (x-4,2 - y -1)$