Find the distance between the points (-1,4) and (-2,-9)

(Distance)^2 = (y2 - y1)^2 + (x2 - x1)^2
= (-13)^2 + (-1)^2 = 170
Distance = sqrt 170 = 13.04

thank you

To find the distance between two points in a coordinate system, you can use the distance formula. The distance formula is derived from the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, the two points are (-1, 4) and (-2, -9). Labeling the first point as (x1, y1) and the second point as (x2, y2), we can plug these values into the distance formula:

Distance^2 = (y2 - y1)^2 + (x2 - x1)^2

Substituting the given values:
Distance^2 = (-9 - 4)^2 + (-2 - (-1))^2
= (-13)^2 + (-2 + 1)^2
= 169 + 1
= 170

Therefore, the squared distance between the two points is 170. To find the actual distance, we need to take the square root of 170:

Distance = sqrt(170)
= 13.04 (rounded to two decimal places)

Hence, the distance between the points (-1, 4) and (-2, -9) is approximately 13.04 units.