Question

Find the distance between the points (-5, 2) and (-6, 10).

You can use the distance formula, but it is not on the formula sheet and is hard to use.

It is easier to plot it on the coordinate plane - Use the Desmos graphing calculator to plot the points, drop the right triangle, and use the Pythagorean Theorem.

(1 point)
Responses

The vertical distance is 8 and the horizontal distance is 1; answer approximately 8.1 units
The vertical distance is 8 and the horizontal distance is 1; answer approximately 8.1 units

The vertical distance is 1 and the horizontal distance is 8; answer approximately 8.1 units
The vertical distance is 1 and the horizontal distance is 8; answer approximately 8.1 units

The vertical distance is 12 and the horizontal distance is 11; answer approximately 16.3 units
The vertical distance is 12 and the horizontal distance is 11; answer approximately 16.3 units

The vertical distance is 11 and the horizontal distance is 12; answer approximately 16.3 units
The vertical distance is 11 and the horizontal distance is 12; answer approximately 16.3 units

Answer 1

To find the distance between the points (-5, 2) and (-6, 10), let's first calculate the vertical and horizontal distances between these points.

1. **Determine the vertical distance (change in y):**
- The y-coordinates are 2 and 10.
- Vertical distance = |10 - 2| = 8.

2. **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.**