#1**0 **

First, know the distance formula:

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

Now, simply substitute the values into this formula and simplify:

\(d=\sqrt{(-6-(-2))^2+(8-(-4))^2}\)

\(=\sqrt{(-6+2)^2+(8+4)^2}\)

\(=\sqrt{(-4)^2+12^2}\)

\(=\sqrt{16+144}\)

\(=\sqrt{160}\)

Of course, put all radicals in simplest radical form. I also included an approximate decimal to the ten thousandths place:

\(\sqrt{160}=\sqrt{16*10}=\sqrt{16}\sqrt{10}=4\sqrt{10}\approx12.6491\)

Let's continue this process for the rest of the points. I'll do the distance from (-2,-4) to (-6,8):

\(d=\sqrt{(-5-(-2))^2+(2-(-4))^2}\)

\(=\sqrt{(5+2)^2+(2+4)^2}\)

\(=\sqrt{7^2+6^2}\)

\(=\sqrt{49+36}\)

\(=\sqrt{85}\approx9.220\)

The square root of 85 is already in simplest radical form, so no need to do anymore.

Guest May 19, 2017

#2**0 **

The previous didn't find the final distance from (-2,-4) to (9,5), so I will:

\(d=\sqrt{(9-(-2))^2+(-5-(-4))^2}\)

\(=\sqrt{(9+2)^2+(-5+4)^2}\)

\(=\sqrt{11^2+(-1)^2}\)

\(=\sqrt{121+1}\)

\(=\sqrt{122}\approx11.0454\)

The square root of 122 has no perfect square factors, so it is already in simplest radical form.

Guest May 19, 2017