Question

1. find the distance between the points (1, 2) and (5, 7).

7.81
2.83
6.40
5.83

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 given points

Here, $x_1 = 1,y_1 = 2,x_2 = 5,y_2 = 7$. So $d=\sqrt{(5 - 1)^2+(7 - 2)^2}=\sqrt{4^2+5^2}$.

Step3: Calculate the squares and sum

$4^2=16$, $5^2 = 25$, then $4^2+5^2=16 + 25=41$. So $d=\sqrt{41}$.

Step4: Find the square - root value

$\sqrt{41}\approx6.40$.

Answer:

6.40