Question

The distance between (3, -6) and (3, -10)

Answer 1

4 units

Explanation:

Since the x-value is the same in both ordered pairs, you can just figure out the y-step (
`y_(2) -y_(1)`) and get your distance. -10 - (-6) = -4, so a distance of 4 units (negative sign does not matter in this case).

If both the x-values and y-values were different, another way to solve is to figure out the y- and x-steps and plug them into the Pythagoras theorem
`A^2+B^2 = C^2`, with A being the horizontal distance (x-step) and B being the vertical distance (y-step).

You can also find the distance between 2 points by using the distance formula, which is
`d = \sqrt{(x_(2)-x_(1))^(2) - (y_(2)-y_(1))^(2)`. After inserting the x- and y-coordinates of your ordered pair you get
`d = \sqrt{(3-3)^(2) - (-10-(-6))^(2)`
Simplifying:

`d = \sqrt{- (-10-(-6))^(2)}`.
`(3-3)^(2)` was eliminated.
Then we distribute the negative signs:
`d = \sqrt{- (-10+6)^(2)}` -->
`d = \sqrt{(10-6)^(2)}`.

`d = \sqrt{(4)^(2)}` -->
`d = √(16)` -->
`d = 4`
So, the distance between the points is 4 units.
Side note: The distance formula works in the same way as the Pythagoras theorem.