Question

calculate the distance between the points f = (1, -1) and b = (9, -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 \( F=(1, -1) \), \( x_1 = 1 \), \( y_1 = -1 \); for \( B=(9, -9) \), \( x_2 = 9 \), \( y_2 = -9 \).

Step3: Substitute into formula

\( d = \sqrt{(9 - 1)^2 + (-9 - (-1))^2} = \sqrt{8^2 + (-8)^2} \)

Step4: Simplify

\( \sqrt{64 + 64} = \sqrt{128} \approx 11.31 \)

Answer:

11.31