Question

Demonstrate the translation of a line segment of 3 units to the left and 5 units down if the endpoints of the line segment are (−2, 7) and (0, 3)

Answer 1

To translate a line segment of 3 units to the left and 5 units down, we need to subtract 3 units from the x-coordinates of the endpoints and subtract 5 units from the y-coordinates.

Given endpoints:
A: (-2, 7)
B: (0, 3)

Translation vector: (-3, -5)

To translate point A, we subtract the translation vector:
A' = (-2 - (-3), 7 - (-5))
A' = (-2 + 3, 7 + 5)
A' = (1, 12)

To translate point B, we also subtract the translation vector:
B' = (0 - (-3), 3 - (-5))
B' = (0 + 3, 3 + 5)
B' = (3, 8)

The translated line segment is defined by the endpoints A' and B':
A': (1, 12)
B': (3, 8)

We can visualize these points and the line segment on a coordinate plane to better understand the translation.