 # What is the average distance between a point in the sebadillab0 2022-07-12 Answered
What is the average distance between a point in the interval [-4,3] and the origin?
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The distance between a point x on the number line and the origin is |x|
We have been asked for the average value of this function on the interval [-4, 3]
We can either evaluate $\frac{1}{3-\left(-4\right)}{\int }_{-4}^{3}|x|dx$ or work through the equivalent geometry without the integral.
The area under graph of |x| and above [=4,3] consists of two isosceles right triangles.
On the left we have a triangle with base and height 4, so its area is 8.
On the right we have a triangle with base and height 3, so its area is $\frac{9}{2}$
The total area under the graph is $\frac{25}{2}$
Divide by the total base of 3+4=7 to get an average value of $\frac{25}{14}$