Point M is the midpoint of AB=6x-2 and MB=4x+4. What is the length of AB?

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21-09-2018
Mathematics

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Point M is the midpoint of AB=6x-2 and MB=4x+4. What is the length of AB?

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jdoe0001 jdoe0001 · Answer 1 · 2018-09-21T01:57:13+02:00

now, if M is the midpoint of AB, that means that the halves of AM and MB are twins.

[tex]\bf \boxed{A}\underset{\leftarrow\qquad 6x-2\qquad \to }{\stackrel{4x+4}{\rule[0.35em]{10em}{0.25pt}} M\stackrel{4x+4}{\rule[0.35em]{10em}{0.25pt}}}\boxed{B} \\\\\\ AB=AM+MB\implies 6x-2=8x+8\implies 10=2x \\\\\\ \cfrac{10}{2}=x\implies 5=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{AB}{6(5)-2}\implies \blacktriangleright 28 \blacktriangleleft[/tex]