+0  
 
0
62
1
avatar

The distance between the points (x,21) and (4,7) is 10sqrt(3) Find the sum of all possible values of x.

 Jan 23, 2022
 #1
avatar+514 
+2

The first step is to consider some triangles.

Once we find x, we can see that there are two congruent triangles with hypotenuse length \(10\sqrt{3}\).

One of the legs of this triangle will be y1 - y2, which is 14.

Using the pythagorean theorem, we can find the distance between the two x coordinates. 

\(\sqrt{(10\sqrt{3})^2 - 14^2}\)

This simplifies to:

\(\sqrt{104}\)

This simplifies to:

\(2\sqrt{26}\)

 

This means the x coordinate is \(2\sqrt{26}\) units away from the x coordinate of (4,7), and then we have these 2 possible values of x:

\(4 + 2\sqrt{26}\) and \(4 - 2\sqrt{26}\)

 

Since the question is looking for the sum of the possible values of x, then we just add the two possible values together:

\(4 + 2\sqrt{26} + 4 - 2\sqrt{26}\)

This simplifies to 8.

 

Therefore, the sum of all possible values of x is 8.

 

 

smiley

 Jan 23, 2022

43 Online Users

avatar