Question

reflect a point across an axis in the coordinate plane. reflect point a across the y - axis. what is the distance from each point to the y - axis? point a distance? point a distance?

Explanation:

Step1: Determine coordinates of Point A

Looking at the graph, Point A is at \( (4, 1) \) (assuming each grid square is 1 unit, since it's 4 units to the right of the y - axis (x = 0) and 1 unit up on the y - axis). The distance from a point \( (x,y) \) to the y - axis is given by \( |x| \). For Point A with \( x = 4 \), the distance is \( |4|=4 \).

Step2: Determine coordinates of Point \( A' \)

Point \( A' \) is the reflection of Point A across the y - axis. The rule for reflecting a point \( (x,y) \) across the y - axis is \( (x,y)\to(-x,y) \). So, if Point A is \( (4,1) \), then Point \( A' \) is \( (- 4,1) \). The distance from Point \( A' \) to the y - axis is \( |-4| = 4 \).

Answer:

For Point A, the distance is 4. For Point \( A' \), the distance is 4.