Question

Garrett reflects points A and B across the y-axis to make the images of the points A' and B'. If the distance between points A and B is 10 units, what is the distance between points A' and B'? Explain your answer.

Answer 1

Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units

Explanation:

Answer 2

• A'B' = AB = 10

Explanation:

Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units

Let the coordinates be:

• A = (x1, y1) and B(x2, y2)

Reflection:

• A'= (-x1, y1) and B(-x2, y2) as per rule

Lets compare distances:

• AB = √(x2-x1)² + (y2 - y1)²

and

• A'B' = √(-x2 - (-x1))² + (y2 - y1)² = √(-(x2 - x1))² + (y2-y1)² = √(x2-x1)² + (y2 - y1)²

As we see the results are same