Use the distance formula and the Pythagorean theorem to find the distance, to the neearest tenth, from R(6,-5) to U(-2,6)

-2 - 6 = -8

6 - (-5) = 11

d = sqrt ( 64 + 121)

what does 'sqrt' stand for?

To find the distance between two points in a coordinate plane, we can use the distance formula. The formula is derived from the Pythagorean theorem, so we can use it to solve this problem.

The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, let's label point R as (x1, y1), which is (6, -5), and point U as (x2, y2), which is (-2, 6).

Substituting the values into the formula, we get:
d = sqrt((-2 - 6)^2 + (6 - (-5))^2)

Simplifying further, we have:
d = sqrt((-8)^2 + (6 + 5)^2)
d = sqrt(64 + 121)
d = sqrt(185)

Now, to find the distance to the nearest tenth, we evaluate the square root to approximate the value:
d ≈ √185
d ≈ 13.6

Therefore, the distance from R(6, -5) to U(-2, 6), rounded to the nearest tenth, is approximately 13.6 units.