I'm here to help you with the length of segment ST given the endpoints S(-7, -6) and T(2, 4). To find the length of a segment with two endpoints in a coordinate plane, we use the distance formula.
1. The distance formula is √[(x2 - x1)^2 + (y2 - y1)^2], where (x1, y1) and (x2, y2) are the coordinates of the two endpoints.
2. For segment ST, the coordinates are:
- S(-7, -6) with x1 = -7 and y1 = -6
- T(2, 4) with x2 = 2 and y2 = 4
3. Plugging the coordinates into the distance formula, we get:
√[(2 - (-7))^2 + (4 - (-6))^2]
= √[(2 + 7)^2 + (4 + 6)^2]
= √[9^2 + 10^2]
= √[81 + 100]
= √181
Therefore, the length of segment ST is √181.
