Question

Line segment FG begins at (-9,-5) and ends at (8,-5). The segment is translated right 10 units and down 7 units to form line segment F’G’. Enter the distance, in units, of line segment F’G’.

Answer 1

The coordinates of F' are (-9+10, -5-7) = (1, -12).

The coordinates of G' are (8+10, -5-7) = (18, -12).

The distance between F' and G' is the same as the distance between F and G, since the translation did not affect the length of the segment perpendicular to the direction of translation.

Using the distance formula:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

d = √[(18 - 1)^2 + (-12 - (-5))^2]

d = √[17^2 + (-7)^2]

d = √(289 + 49)

d = √338

d ≈ 18.38

Therefore, the distance of line segment F'G' is approximately 18.38 units.