Question

Which expression gives the distance between the points (5, 1) and (9, -6)?

Answer 1

Answer:

$d = \sqrt{65}\text{ units}$

Step-by-step explanation:

Let $(x_1,x_2)$ and $(y_1, y_2)$ be the two points.

We have to find the distance between the two points.

The distance Formula:

$d = \sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2}$

Here, we are given $(x_1,x_2)$ = (5,1) and  $(y_1, y_2)$  = (9,-6)

Then, the distance between these two points is given by:

$d = \sqrt{(5 - 9)^2 + (1- (-6))^2}$

$d = \sqrt{(-4)^2 + (7)^2}$

$d = \sqrt{16 + 49}$

$d = \sqrt{65}$

Thus, the distance between the given point is $\sqrt{65}\text{ units}$.

Answer 2

So the distance formula: d = rad (x2 - x1)^2 + (y2 - y1)^2
it doesn't matter what order you do, you just have to make sure it's a y coordinate for y and an x coordinate for x.
rad (9-5)^2 + ((-6)-1)^2
rad 4^2 + (-7)^2
rad 16 + 49
rad 65