Question

Distance between (2,10) and (-1,10)

Answer 1

Take a look at the two points and their coordinates.

Both points have the same y coordinates. That means the two points will be in line horizontally across the y axis.

That means, to work out the distance between the two points, all you have to do is find the difference in the x-coordinates of the two points, like so:

Distance = difference in x-coordinates

= 2 - - 1

= 2 + 1

= 3

So the distance between (2, 10) and (-1, 10) is: 3

- - - - - - - - - - - - - - - - - - -

Answer: 3

- - - - - - - - - - - - - - - - - - -

Note: this method only works if the two points share either the same x-coordinates, or the same y-coordinates.

If you want to know how to work out distance between two points when this is not the case, then read on below. If not, no need to read on.

_______________________________________________________

How to work out distance between two points, when they don't share either the same x or y coords.

To work out the distance between two points, you can make a right angled triangle.

Since the triangle is right angled, we can use Pythagoras' theorem to work out the hypotenuse (which is the distance from the two coordinates).

(picture is attached to help with visualisation of this)

Pythagoras' Theorem is :

`hypotenuse = \sqrt{height^(2) +base^(2)}`

To use the formula, we first need to work out the height and the base of the right angled triangle.

So to work out the height and base, we find the difference in the y and x coordinates of two points:

Height = difference in y coordinates = 10 - 10 = 0

Base = difference in x coordinates = 2 - - 1 = 2 + 1 = 3

Now we just substitute in the values for the height and base in the Pythagorean theorem:

`hypotenuse = \sqrt{height^(2) +base^(2)}`

`Distance= \sqrt{0^(2) + 3^(2)}`

`Distance= √(0 + 9 )`

`Distance= 3`

So the distance between the two points is 3

Answer 2

The distance is 10!

Hope this helps. Good luck!! You got this :)