Question

calculate the distance between the points f=(1, -6) and b=(4, -9) in the coordinate plane. round your answer to the nearest hundredth. image of coordinate plane with points f and b distance: blank

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, \( x_1 = 1,y_1=-6,x_2 = 4,y_2=-9 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1=4 - 1 = 3 \) and \( y_2 - y_1=-9-(-6)=-9 + 6=-3 \). Then, substitute these into the formula: \( d=\sqrt{(3)^2+(-3)^2} \).

Step3: Simplify the expression inside the square root

Calculate \( (3)^2 = 9 \) and \( (-3)^2 = 9 \), so \( d=\sqrt{9 + 9}=\sqrt{18} \).

Step4: Calculate the square root and round

\( \sqrt{18}\approx4.2426 \), and rounding to the nearest hundredth gives \( 4.24 \).

Answer:

\( 4.24 \)