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.
Reflection Rotation 89C011
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.