Question

(2, 7) and (-6, -2) find the distance between each pair of points

Answer 1

Answer:

$\sqrt{145}$

Step-by-step explanation:

Hi there!

We are given the points (2, 7) and (-6, -2). We want to find the distance between them. To do that, we can use the distance formula

The distance formula is given as $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points

We have 2 points, which is what we need to find the distance, but let's label their values to avoid any confusion

$x_1=2\\y_1=7\\x_2=-6\\y_2=-2$

Now substitute those values into the formula:

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

$\sqrt{(-6-2)^2+(-2-7)^2}$

Simplify the values under the radical:

$\sqrt{(-8)^2+(-9)^2}$

Raise to the second power:

$\sqrt{64+81}$

Add the numbers under the radical together

$\sqrt{145}$

The answer can be left as that, as the radical cannot be simplified.

Hope this helps!