Answer:
[tex]\sqrt{145}[/tex]
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 [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] 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
[tex]x_1=2\\y_1=7\\x_2=-6\\y_2=-2[/tex]
Now substitute those values into the formula:
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{(-6-2)^2+(-2-7)^2}[/tex]
Simplify the values under the radical:
[tex]\sqrt{(-8)^2+(-9)^2}[/tex]
Raise to the second power:
[tex]\sqrt{64+81}[/tex]
Add the numbers under the radical together
[tex]\sqrt{145}[/tex]
The answer can be left as that, as the radical cannot be simplified.
Hope this helps!
