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K is the midpoint of AB, if AK = 4x+3 and KB =7x=3 , find the length of AB

1 Answer

1 vote
I'm assuming you meant to write
7x-3 instead... If so,
AB=22.

Because
K is the midpoint of
AB,
AK must equal
KB.

Set the two equal to each other and solve for
x...


4x+3=7x-3 \\ 4x+6=7x \\ 6=3x \\ x=2

Now plug
2 in for
x in either
AK or
KB.


AK=4(2)+3=8+3=11

or


KB=7(2)-3=14-3=11

Now we know half of the length of
AB. Multiplying
11 by
2 will give us the full length, which is
22.
User Dveim
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