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.
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.
