Question

1. find the distance between the two points in simplest form. (7,1) and (4,5)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 7,y_1 = 1,x_2 = 4,y_2 = 5$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=4 - 7=- 3$ and $y_2 - y_1=5 - 1 = 4$.

Step3: Square the differences

Square the results from Step 2. $(-3)^2=9$ and $4^2 = 16$.

Step4: Sum the squared differences

Add the squared - values: $9 + 16=25$.

Step5: Take the square root

$d=\sqrt{25}=5$.

Answer:

5