AB has endpoints A(-3,2) and B(3,-2). Find AB to the tenth. The answer is 2 square root 13. I want to know how to get the answer. What the steps to finding the answer?

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mfonda's profile pic

Matthew Fonda | eNotes Employee

Posted on

AB is a line segment that we know the start point and end point of. We know from the Pythagorean theorem that the length of the hypotenuse of triangle is given by

`c = sqrt(a^2 + b^2)`

Using our points, let's construct a triangle where the hypotenuse is the line segment AB. To form the base of our triangle, we subtract the two x distances:

`a = -3 - 3 = -6`

We do the same thing for the y distances:

`b = 2 - -2 = 4`

We can then evaluate the distance using the Pythagorean theorem:

`c = sqrt(a^2 + b^2)`

`= sqrt((-6)^2 + 4^2)`

`= sqrt(36 + 16)`

`= sqrt(52)`

`= sqrt(4 * 13)`

`= sqrt(4) * sqrt(13)`

`= 2sqrt(13)`


Note: there was previously an aritmetic mistake above. This has been corrected.

The formula we derived is known as the distance formula for a line segment, and is usually given by

`d = sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)`

embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

There is an arithmetic mistake in the answer above.

`sqrt(36+16)=sqrt(52)=sqrt(4*13)=sqrt(4)sqrt(13)=2sqrt(13)` .

In your question you asked about AB to the tenth; I believe you want the answer to the nearest tenth. `2sqrt(13)` is the exact answer, while 7.2 is the approximate answer to the nearest tenth.

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