Final answer:
The distance between the points (-15,7) and (5,-4) is found using the distance formula. After calculating the squares of the changes in x and y, and adding them together, the square root of the sum is taken and rounded to the nearest hundredth. The result is approximately 22.83 units.
Step-by-step explanation:
To find the distance between the points (-15,7) and (5,-4), we use the distance formula derived from the Pythagorean theorem, which is distance = √((x2 - x1)² + (y2 - y1)²). In this case, (x1, y1) = (-15,7) and (x2, y2) = (5,-4).
First, we calculate the change in x (x2 - x1) and the change in y (y2 - y1):
- Change in x = 5 - (-15) = 5 + 15 = 20
- Change in y = -4 - 7 = -11
Next, we square each change and add them together:
- x² = 20² = 400
- y² = (-11)² = 121
- Sum = 400 + 121 = 521
Then, we take the square root of this sum to get the distance:
√521 ≈ 22.825
Finally, we round this value to the nearest hundredth:
The distance is approximately 22.83 units (rounded to the nearest hundredth).