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Sreve: Da $\newline$ fenativen: of $4$ $\newline$ veranes $\newline$ Question $\newline$ Watch Video $\newline$ Show Examples $\newline$ stera be chanchat $\newline$ aretrivarian $\newline$ thetereation $\newline$ Answer Aftempt $1$ out of $2$ $\newline$ What is the image point of $\newline$ $(-6,-1)$ after the transformation $\newline$ $R_{180}@r_{y=-x}$ ? $\newline$ $(1)$ $\newline$ Submit Answer

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Q. Sreve: Da

\newline

fenativen: of

4

\newline

veranes

\newline

Question

\newline

Watch Video

\newline

Show Examples

\newline

stera be chanchat

\newline

aretrivarian

\newline

thetereation

\newline

Answer Aftempt

1

out of

2

\newline

What is the image point of

\newline

(-6,-1)

after the transformation

\newline

R_{180}@r_{y=-x}

?

\newline

(1)

\newline

Submit Answer

Understand Transformation $R_{180}@r_{y=-x}$ : First, let's understand the transformation $R_{180}@r_{y=-x}$ . This notation indicates a composition of two transformations: a rotation of $180$ degrees ( $R_{180}$ ) and a reflection across the line $y = -x$ ( $r_{y=-x}$ ). We need to apply these transformations to the point $(-6,-1)$ in the given order.
Apply Reflection Across $y=-x$ : Let's start with the reflection across the line $y = -x$ . To reflect a point across this line, we swap the $x$ and $y$ coordinates and change their signs. So, the reflection of $(-6,-1)$ would be $(1,6)$ .
Perform Rotation of ext{ $180$ } Degrees: Now, we need to perform the rotation of ext{ $180$ } degrees ( ext{ $R_{180}$ }). Rotating a point ext{ $180$ } degrees around the origin ext{ $(0,0)$ } will change the signs of both coordinates. So, the rotation of ext{ $(1,6)$ } will result in ext{ $(-1,-6)$ }.
Final Image Point: After performing both transformations, the image point of $(-6,-1)$ is $(-1,-6)$ . This is the final answer.

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