Final answer:
To find point T, we can use the distance formula and Pythagorean theorem. The coordinates of T are (2, -5).
Step-by-step explanation:
To find point T, we need to determine the coordinates of the third vertex of triangle RST. Given that R is (-4, -1) and S is (2, -5), we can use the distance formula and Pythagorean theorem to find the coordinates of T.
1. Find the length of RS using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) = R and (x2, y2) = S. In this case, d = √((2 - (-4))^2 + (-5 - (-1))^2) = √(6^2 + (-4)^2) = √(36 + 16) = √52.
2. Since RS is the hypotenuse of the right triangle RST, we can use the Pythagorean theorem to find the coordinates of T. The lengths of the legs of the triangle are the differences between the x-coordinates and the y-coordinates of R and S: x-leg = x2 - x1 = 2 - (-4) = 6 and y-leg = y2 - y1 = -5 - (-1) = -4.
3. The coordinates of T can be found by adding the lengths of the legs to the coordinates of R: (x-coordinate, y-coordinate) = (x1 + x-leg, y1 + y-leg) = (-4 + 6, -1 + (-4)) = (2, -5).