Question

question 20. find the distance between (-3, -11) and (8, -42). a. 32.3 b. 32.9 c. 32.7 d. 32.1

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, \(x_1=-3\), \(y_1 = - 11\), \(x_2 = 8\), \(y_2=-42\).

Step2: Calculate the differences in coordinates

First, find \(x_2 - x_1\): \(8-(-3)=8 + 3=11\).
Then, find \(y_2 - y_1\): \(-42-(-11)=-42 + 11=-31\).

Step3: Square the differences

Square of \(x_2 - x_1\): \(11^2 = 121\).
Square of \(y_2 - y_1\): \((-31)^2=961\).

Step4: Sum the squares

Sum \(121+961 = 1082\).

Step5: Take the square root

\(d=\sqrt{1082}\approx32.9\) (rounded to one decimal place).

Answer:

B. 32.9