Final answer:
To find the distance between point D(-6, -2) and point T(7, -8) using the Pythagorean theorem, determine the distance in the x-direction and y-direction, then use the formula c^2 = a^2 + b^2 to calculate the length of the hypotenuse.
Step-by-step explanation:
To find the distance between point D(-6, -2) and point T(7, -8) using the Pythagorean theorem, we need to calculate the length of the hypotenuse of the right triangle formed by the two points.
Step 1: Determine the distance in the x-direction by subtracting the x-coordinate of D from the x-coordinate of T: 7 - (-6) = 13.
Step 2: Determine the distance in the y-direction by subtracting the y-coordinate of D from the y-coordinate of T: -8 - (-2) = -6.
Step 3: Use the Pythagorean theorem (a^2 + b^2 = c^2) to find the length of the hypotenuse: c^2 = 13^2 + (-6)^2.
Step 4: Simplify the equation: c^2 = 169 + 36 = 205.
Step 5: Take the square root of both sides to find the length of the hypotenuse: c = √205 ≈ 14.317.
Therefore, the distance between D(-6, -2) and T(7, -8) is approximately 14.317 units.