Question

2.) determine the distance: (-1,2) and (3,5)

Explanation:

Step1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
Here, \( x_1=-1 \), \( y_1 = 2 \), \( x_2=3 \), \( y_2 = 5 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1=3-(-1)=3 + 1=4 \) and \( y_2 - y_1=5 - 2 = 3 \).
Then, substitute these into the formula: \( d=\sqrt{(4)^2+(3)^2} \).

Step3: Simplify the expression

Calculate \( 4^2 = 16 \) and \( 3^2=9 \), so \( d=\sqrt{16 + 9}=\sqrt{25} \).

Step4: Evaluate the square root

\( \sqrt{25}=5 \).

Answer:

5