Question

list the coordinates of the figure. then list the coordinates after a reflection over the y-axis.

Explanation:

Step1: Identify Original Coordinates

To find the coordinates of a point \((x, y)\) on the coordinate plane, the \( x \)-coordinate is the horizontal distance from the \( y \)-axis, and the \( y \)-coordinate is the vertical distance from the \( x \)-axis.

• For \( Q \): Moving 2 units right (positive \( x \)) and 1 unit up (positive \( y \)) from the origin, so \( Q = (2, 1) \).
• For \( R \): Moving 1 unit right and 5 units up, so \( R = (1, 5) \).
• For \( V \): Moving 4 units right and 5 units up, so \( V = (4, 5) \).
• For \( T \): Moving 5 units right and 1 unit up, so \( T = (5, 1) \).

Step2: Apply Reflection over \( y \)-axis

The rule for reflecting a point \((x, y)\) over the \( y \)-axis is \((x, y) \to (-x, y)\) (the \( y \)-coordinate remains the same, and the \( x \)-coordinate is negated).

• For \( Q(2, 1) \): Apply the rule: \( (2, 1) \to (-2, 1) \), so \( Q' = (-2, 1) \).
• For \( R(1, 5) \): Apply the rule: \( (1, 5) \to (-1, 5) \), so \( R' = (-1, 5) \).
• For \( V(4, 5) \): Apply the rule: \( (4, 5) \to (-4, 5) \), so \( V' = (-4, 5) \).
• For \( T(5, 1) \): Apply the rule: \( (5, 1) \to (-5, 1) \), so \( T' = (-5, 1) \).

Answer:

Original Coordinates:

• \( Q: (2, 1) \)
• \( R: (1, 5) \)
• \( V: (4, 5) \)
• \( T: (5, 1) \)

After Reflection over \( y \)-axis:

• \( Q': (-2, 1) \)
• \( R': (-1, 5) \)
• \( V': (-4, 5) \)
• \( T': (-5, 1) \)