Final answer:
The distance between the two points (6,-5) and (-30,155) is found using the distance formula, resulting in a distance of 164 units.
Step-by-step explanation:
To find the distance between the two points (6,-5) and (-30,155), we use the distance formula derived from the Pythagorean theorem.
This formula is d = √((x2-x1)^2 + (y2-y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging the values into the formula, we perform the following steps:
Calculate the difference in the x-coordinates:
(-30) - (6) = -36.
Calculate the difference in the y-coordinates:
(155) - (-5) = 160.
Square both differences:
(-36)^2 = 1296 and (160)^2 = 25600.
Add the squares of the differences:
1296 + 25600 = 26896.
Take the square root of the sum:
√26896 = 164.
The distance between the two points is 164 units.