Question

calculate the distance between the points h = (-3, -2) and p = (1, -9) 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 \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step2: Identify coordinates

For \( H(-3, -2) \) and \( P(1, -9) \), \( x_1 = -3 \), \( y_1 = -2 \), \( x_2 = 1 \), \( y_2 = -9 \).

Step3: Substitute into formula

Calculate \( x_2 - x_1 = 1 - (-3) = 4 \), \( y_2 - y_1 = -9 - (-2) = -7 \).
Then \( d = \sqrt{(4)^2 + (-7)^2} = \sqrt{16 + 49} = \sqrt{65} \).

Step4: Compute and round

\( \sqrt{65} \approx 8.06 \) (rounded to nearest hundredth).

Answer:

8.06