Question

The points A(-3,-2) and B(0,-8) on a coordinate plane. The points undergo the same rigid transformation to create the points A' and B: What is the distance, in units, between point A' and point B'? Round your answer to the nearest tenth.

Answer 1

The distance between points A' and B' after a rigid transformation, which preserves distances between points, is approximately 6.7 units.

Step-by-step explanation:

The question asks for the distance between points A' and B' after a rigid transformation is applied to points A and B. In rigid transformations, the distance between points remains the same. Therefore, the distance between A' and B' will be the same as the distance between A and B originally. To find this distance, we can use the distance formula which is d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Applying the formula to points A(-3, -2) and B(0, -8), we calculate the distance as follows:

• x1 = -3, y1 = -2
• x2 = 0, y2 = -8
• d = √((0 - (-3))² + (-8 - (-2))²)
• d = √((3)² + (-6)²)
• d = √(9 + 36)
• d = √45
• d ≈ 6.7 units

So, the distance between points A' and B' after the rigid transformation is approximately 6.7 units.