Question

find the length of a segment with endpoints (15.3, 18.1) and (-8.8, -13.6) to the nearest hundredth.

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, \(x_1 = 15.3\), \(y_1=18.1\), \(x_2=- 8.8\), \(y_2=-13.6\).

Step2: Calculate the differences in coordinates

First, find \(x_2 - x_1\): \(-8.8-15.3=-24.1\)
Then, find \(y_2 - y_1\): \(-13.6 - 18.1=-31.7\)

Step3: Square the differences

Square of \(-24.1\): \((-24.1)^2 = 24.1\times24.1 = 580.81\)
Square of \(-31.7\): \((-31.7)^2=31.7\times31.7 = 1004.89\)

Step4: Sum the squared differences

\(580.81 + 1004.89=1585.7\)

Step5: Take the square root

\(d=\sqrt{1585.7}\approx39.82\) (rounded to the nearest hundredth)

Answer:

\(39.82\)