Question

Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.

a) Distance AB
b) Distance A'B'
c) Distance AA'
d) Distance BB'
e) Distance CC'

Answer 1

To find the distance A'B', apply the transformation T to the coordinates of point A' and B' and calculate the distance between the transformed points using the distance formula.

Step-by-step explanation:

To find the distance A'B', we need to apply the transformation T to the coordinates of point A' and point B' and then calculate the distance between the transformed points. For point A' = (-1, -3), applying the transformation T gives A' = (-1 + 2, -3 + 1) = (1, -2). For point B' = (-4, 5), applying the transformation T gives B' = (-4 + 2, 5 + 1) = (-2, 6). The distance between A' and B' can be calculated using the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates, we have:

d = sqrt((-2 - 1)^2 + (6 - (-2))^2) = sqrt((-3)^2 + (8)^2) = sqrt(9 + 64) = sqrt(73).