Question

calculate the distance between the points k=(0, -9) and m=(5, -4) in the coordinate plane. round your answer to the nearest hundredth.

Explanation:

Step1: Recall distance formula

The distance \( d \) 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, \( x_1 = 0, y_1 = -9, x_2 = 5, y_2 = -4 \).

Step2: Substitute values into formula

Calculate \( x_2 - x_1 = 5 - 0 = 5 \) and \( y_2 - y_1 = -4 - (-9) = -4 + 9 = 5 \).

Step3: Compute squares and sum

\( (x_2 - x_1)^2 = 5^2 = 25 \), \( (y_2 - y_1)^2 = 5^2 = 25 \). Sum: \( 25 + 25 = 50 \).

Step4: Take square root and round

\( d = \sqrt{50} \approx 7.07 \) (rounded to nearest hundredth).

Answer:

7.07