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 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 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 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 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), we can use the vertical and horizontal distances to form a right triangle and apply the Pythagorean theorem.

1. **Calculate the vertical distance**:
- The y-coordinates of the points are 2 and 10.
- Vertical distance = |10 - 2| = 8.

2. **Calculate the horizontal distance**:
- The x-coordinates of the points are -5 and -6.
- Horizontal distance = |-6 - (-5)| = |-6 + 5| = 1.

3. **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.**