Question

Which expression represents the difference between (0, a) and point (a, 0) on a coordinate grid?

Answer 1

`√(2)a`

Explanation:

Suppose we have two points:

`A = (x_(1), y_(1))`

`B = (x_(2), y_(2))`

The distance between these points is:

`D = \sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)}`

In this question:

We have to find the difference between these two points.

(0, a) and (a,0). So

`D = \sqrt{(a - 0)^(2) + (0 - a)^(2)} = \sqrt{a^(2) + a^(2)} = \sqrt{2a^(2)} = \sqrt{a^(2)}√(2) = √(2)a`

So the answer is:

`√(2)a`