To find the distance between the points (-5, 2) and (-6, 10), let's first calculate the vertical and horizontal distances between these points.
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Determine the vertical distance (change in y):
- The y-coordinates are 2 and 10.
- Vertical distance = |10 - 2| = 8.
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Determine the horizontal distance (change in x):
- The x-coordinates are -5 and -6.
- Horizontal distance = |-6 - (-5)| = |-6 + 5| = |-1| = 1.
Now, we have:
- Vertical distance = 8
- Horizontal distance = 1
Now we can use the Pythagorean theorem to find the distance \(d\): \[ d = \sqrt{(\text{horizontal distance})^2 + (\text{vertical distance})^2} = \sqrt{(1)^2 + (8)^2} = \sqrt{1 + 64} = \sqrt{65} \approx 8.06. \]
Given this information, the closest response is:
The vertical distance is 8 and the horizontal distance is 1; answer approximately 8.1 units.