To find the distance between the points (-5, 2) and (-6, 10), we can use the vertical and horizontal distances to form a right triangle and apply the Pythagorean theorem.
-
Calculate the vertical distance:
- The y-coordinates of the points are 2 and 10.
- Vertical distance = |10 - 2| = 8.
-
Calculate the horizontal distance:
- The x-coordinates of the points are -5 and -6.
- Horizontal distance = |-6 - (-5)| = |-6 + 5| = 1.
-
Use the Pythagorean theorem:
- \(d = \sqrt{(horizontal \ distance)^2 + (vertical \ distance)^2}\)
- \(d = \sqrt{(1)^2 + (8)^2}\)
- \(d = \sqrt{1 + 64} = \sqrt{65} \approx 8.1\) units.
Thus, the correct answer is: The vertical distance is 8 and the horizontal distance is 1; answer approximately 8.1 units.