Question

How do you find the distance between point A(-3, 5) and point B(4, -6) in the coordinate plane?

Answer 1

`d(A,B)=sqrt(170)~~13.03`.

Explanation:

Having the points `A(-3,5) and B(4,-6)` on the same plane.
We calculate the distance d with the formula:
`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`.
So in this case we have:
`d=sqrt((4-(-3))^2+(-6-5)^2)=sqrt(49+121)=sqrt(170)~~13.03`

Answer 2

You first work out the `x`- and `y`-distances and then use Pythagoras

Explanation:

In the horizontal (x) direction the distance is:
`Deltax=4-(-3)=7`
In the vertical (y) direction the distance is:
`Deltay=-6-5=-11` or just plain `11`
(you should draw this on coordinate paper)

We now have a right-sided triangle, where the hypotenuse is the distance between A and B.

So `(AB)^2=(Deltax)^2+(Deltay)^2->`
`(AB)^2=7^2+11^2=49+121=170->`
`AB=sqrt170~~13.0`

Answer 3

Find distance between A (-3, 5) and B (4, -6)

Explanation:

Use formula for distance: `d^2 = (x2 - x1)^2 + (y2 - y1)^2`

`d^2 = (4 + 3)^2 + (-6 - 5)^2 = 49 + 121 = 170`

d = 13.04