if -5,6 is reflected in the line y=-x theb rotated 180 about the point -7,2 what are the coordinates?

Reflect Point in Line: Reflect the point (-5, 6) in the line y = -x. To reflect a point across the line y = -x, we swap the x and y coordinates and change their signs. So, the reflection of (-5, 6) is (6, -5).Check Reflection: Check the reflection for any mathematical errors. Original point: (-5, 6) Reflected point: (6, -5) The reflection swaps and negates the coordinates correctly.Rotate Point 180 Degrees: Rotate the reflected point (6, -5) 180 degrees about the point (-7, 2). Rotating a point 180 degrees around another point means the point will be on the opposite side of the center point and at the same distance. To find the new coordinates, we calculate the differences in x and y, double them, and subtract from the center point's coordinates. Difference in x: 6 - (-7) = 13 Difference in y: -5 - 2 = -7 New x-coordinate: -7 - (2 * 13) = -7 - 26 = -33 New y-coordinate: 2 - (2 * -7) = 2 + 14 = 16Check Rotation: Check the rotation for any mathematical errors. Differences calculated: (13, -7) Doubled differences: (26, 14) New coordinates: (-33, 16) The rotation calculations are correct.

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if $-5,6$ is reflected in the line $y=-x$ then rotated $180^\circ$ about the point $-7,2$ what are the coordinate?

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Q. if

-5,6

is reflected in the line

y=-x

then rotated

180^\circ

about the point

-7,2

what are the coordinate?

Reflect Point in Line: Reflect the point $(-5, 6)$ in the line $y = -x$ . To reflect a point across the line $y = -x$ , we swap the $x$ and $y$ coordinates and change their signs. So, the reflection of $(-5, 6)$ is $(6, -5)$ .
Check Reflection: Check the reflection for any mathematical errors. $\newline$ Original point: $(-5, 6)$ $\newline$ Reflected point: $(6, -5)$ $\newline$ The reflection swaps and negates the coordinates correctly.
Rotate Point $180$ Degrees: Rotate the reflected point $(6, -5)$ $180$ degrees about the point $(-7, 2)$ . Rotating a point $180$ degrees around another point means the point will be on the opposite side of the center point and at the same distance. To find the new coordinates, we calculate the differences in $x$ and $y$ , double them, and subtract from the center point's coordinates. Difference in $x$ : $6 - (-7) = 13$ Difference in $y$ : $-5 - 2 = -7$ New $x$ -coordinate: $-7 - (2 \times 13) = -7 - 26 = -33$ New $y$ -coordinate: $(-7, 2)$ $1$
Check Rotation: Check the rotation for any mathematical errors. $\newline$ Differences calculated: $(13, -7)$ $\newline$ Doubled differences: $(26, 14)$ $\newline$ New coordinates: $(-33, 16)$ $\newline$ The rotation calculations are correct.