Question 1207839
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Let's find the distance from A to B.
A = (x1,y1) = (-4,6)
B = (x2,y2) = (-1,2)
{{{d = sqrt( (x1-x2)^2 + (y1-y2)^2 )}}}


{{{d = sqrt( (-4-(-1))^2 + (6-2)^2 )}}}


{{{d = sqrt( (-4+1)^2 + (6-2)^2 )}}}


{{{d = sqrt( (-3)^2 + (4)^2 )}}}


{{{d = sqrt( 9 + 16 )}}}


{{{d = sqrt( 25 )}}}


{{{d = 5}}}
The distance from A to B is exactly 5 units.
Therefore, segment AB is 5 units long.


Follow similar steps to compute the length of BC.
I'll let the student do this part.
You should get BC = 5 as the result. 
This will prove AB = BC.


I'll also leave the scratch work for computing the length of AC to the student.
You should get AC = 10


This confirms that AB+BC = AC is the case since 5+5 = 10.
Since AB = BC, we have proven that B is the midpoint of AC.


Side note: The equation 4x+3y = 2 goes through points A,B, and C.
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