Subjects geometry

Reflection Rotation 89C011

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1. **Problem 1A: Reflecting point P over the x-axis** The original point P is at coordinates $P(3,5)$. When reflecting a point over the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign. Formula for reflection over x-axis: $$P'(x,y) = (x, -y)$$ Applying this to point P: $$P'(3,5) = (3, -5)$$ So, the location of $P'$ after reflection over the x-axis is $(3, -5)$. 2. **Problem 1B: Rotating point R 90 degrees clockwise about the origin** The original point R is at coordinates $R(7,2)$. A 90-degree clockwise rotation about the origin transforms a point $(x,y)$ to $(y, -x)$. Formula for 90-degree clockwise rotation: $$R'(x,y) = (y, -x)$$ Applying this to point R: $$R'(7,2) = (2, -7)$$ So, the location of $R'$ after a 90-degree clockwise rotation is $(2, -7)$. **Final answers:** - $P' = (3, -5)$ after reflection over the x-axis. - $R' = (2, -7)$ after 90-degree clockwise rotation.