Question

4. Tavon claims that d = sqrt((x_{1} - x_{2}) ^ 2 + (y_{1} - y_{2}) ^ 2) can also be used to find the distance between two points. Is he correct? Explain.

Answer 1

yes; the sign of a value being squared is irrelevant

Explanation:

You want to know if the formula d = sqrt((x_{1} - x_{2})^2 + (y_{1} - y_{2})^2) can be used to find the distance between (x_1, y_1) and (x_2, y_2).

Distance formula

The formula for the distance between two points is usually written ...

`d=√((x_2-x_1)^2+(y_2-y_1)^2)\qquad\text{distance between $(x_1,y_1)$ and $(x_2,y_2)$}`

We know that ...

`(x_2-x_1)^2 = (x_1-x_2)^2 = x_1^2+x_2^2-2x_1x_2`

That is, the sign of the difference between corresponding coordinates is irrelevant.

Tavon is correct.