Answer:
[tex]\sqrt{65}[/tex]
Step-by-step explanation:
Hi there!
We want to find the distance between the points (7, 2) and (6, 10).
We can use the distance formula for that, which is [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 the two points needed to find the formula, let's label their values to avoid confusion
[tex]x_1=7\\y_1=2\\x_2=6\\y_2=10[/tex]
Now substitute those values into the formula
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{(6-7)^2+(10-2)^2}[/tex]
Now, under the radical, simplify the values in parentheses
[tex]\sqrt{(-1)^2+(8)^2}[/tex]
Now raise the values under the radical
[tex]\sqrt{1+64}[/tex]
Add the values under the radical together
[tex]\sqrt{65}[/tex]
It's always good to simplify the radical if possible, but in this case, we can't. So [tex]\sqrt{65}[/tex] is the answer.
Hope this helps!
