Answer & Step-by-step explanation:
First, we must know the formula for finding the distance between two given points.
[tex]Distance(d)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We will plug in (2,2) for (x1,y1) and we will plug in (5,5) for (y2,y1).
[tex]Distance(d)=\sqrt{(5-2)^2+(5-2)^2}[/tex]
Subtract 2 from 5 in both parentheses.
[tex]Distance(d)=\sqrt{(3)^2+(3)^2}[/tex]
Simplify the exponents.
[tex]Distance(d)=\sqrt{9+9}[/tex]
Add 9 and 9 together.
[tex]Distance(d)=\sqrt{18}[/tex]
Simplify the radical.
[tex]Distance(d)=3\sqrt{2}[/tex]
This number can also be simplified into 4.24.
So, the distance between the two points is 3√2 units or 4.24 units.
