Question

find the distance between the points a and b given below. (that is, find the length of the segment connecting a and b.) round your answer to the nearest hundredth.

Explanation:

Step1: Determine the horizontal and vertical distances

Count the horizontal \( \Delta x \) and vertical \( \Delta y \) distances between \( A \) and \( B \). Assume \( A(x_1,y_1) \) and \( B(x_2,y_2) \). From the grid, \( \Delta x=x_2 - x_1 = 5 \) units and \( \Delta y=y_2 - y_1= 7 \) units.

Step2: Apply the distance formula

The distance formula is \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). Substitute \( \Delta x = 5 \) and \( \Delta y = 7 \) into the formula: \( d=\sqrt{5^2 + 7^2}=\sqrt{25+49}=\sqrt{74} \).

Step3: Calculate the numerical value

\( \sqrt{74}\approx8.6023 \). Rounding to the nearest hundredth gives \( d\approx8.60 \).

Answer:

\( 8.60 \)