To find the perimeter of the triangle with vertices (1,-5), (4,2), and (-7,-5), we need to find the distance between each pair of points and add them up.
Using the distance formula, we find:
- The distance between (1,-5) and (4,2) is sqrt[(4-1)^2 + (2-(-5))^2] = sqrt[3^2 + 7^2] = sqrt[58].
- The distance between (4,2) and (-7,-5) is sqrt[(-7-4)^2 + (-5-2)^2] = sqrt[(-11)^2 + (-7)^2] = sqrt[170].
- The distance between (-7,-5) and (1,-5) is sqrt[(1-(-7))^2 + (-5-(-5))^2] = sqrt[8^2] = 8.
Adding these distances together, we get:
sqrt[58] + sqrt[170] + 8
This is the perimeter of the triangle. We can simplify it by leaving it in terms of radicals, or by using a calculator to get a decimal approximation.