Question

what is the distance between (-5, 0) and (0, 3)? round your answer to 2 decimal places, if needed.

Explanation:

Step1: Recall 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, \( x_1=-5,y_1 = 0,x_2=0,y_2=3 \).

Step2: Substitute values into formula

Substitute the values into the formula:
\( d=\sqrt{(0 - (-5))^2+(3 - 0)^2}=\sqrt{(5)^2+(3)^2} \)

Step3: Calculate the squares

Calculate \( 5^2 = 25 \) and \( 3^2=9 \), so \( d=\sqrt{25 + 9}=\sqrt{34} \)

Step4: Compute the square root

\( \sqrt{34}\approx5.83 \) (rounded to two decimal places)

Answer:

\( 5.83 \)