1. what is the length of the points (2,5) and (7,8)?

Explanation:

Step1: Identify distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Substitute the values

Here, $x_1 = 2,y_1 = 5,x_2 = 7,y_2 = 8$. So $d=\sqrt{(7 - 2)^2+(8 - 5)^2}=\sqrt{5^2+3^2}$.

Step3: Calculate the squares and sum

$5^2=25$, $3^2 = 9$, then $5^2+3^2=25 + 9=34$. So $d=\sqrt{34}$.

Answer:

$\sqrt{34}$