Question

What is the distance for A(6,0), B (-4,5)

Answer 1

`5√(5)`

Explanation:

The distance formula states that
`D(x_(1) ,y_(1))(x_(2),y_(2) )=\sqrt{(x_(2) } -x_(1) )^2+(y_(2)-y_(1) )^2\\`

We plug in our points, (6,0) and (-4,5), and compute.

`√((-4-6)^2+(5-0)^2) \\√((-10)^2+5^2) \\√(100+25) \\√(125) \\5√(5)` (Make sure you see why I put parentheses around the -10 in (-10)^2. -x^2 and (-x)^2 are not the same) (Also here is why the simplification of the radical works)

`√(125) =√(5^2*5) =√(5^2) *√(5) =5*√(5) =5√(5)`

The * stands for multiplication.