Question

Find Distance (4,6) (-4,-3)​

Answer 1

`√(145)`

Explanation:

The distance formula states that the distance between two points
`(a,b)` and
`(c,d)` is
`√((a-c)^2+(b-d)^2)`.

The two points we have are
`(4,6)` and
`(-4,-3)`. Plugging these numbers into the distance formula, we have

`\sqrt{(4-(-4))^2+(6-(-3))^2`.

Simplifying with order of operations, first using the distributive property, gives

`\sqrt{(4+4)^2+(6+3)^2`.

Squaring and adding gives

`√((4+4)^2+(6+3)^2)=√(8^2+9^2)\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~=√(64+81)\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\boxed{√(145)},`

which is the answer in simplest form. This also rounds to about 12.04.