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Sagot :
Given:
B is the midpoint of line AC.
[tex]AB=6Y-14[/tex]
[tex]BC=10-2Y[/tex]
To find:
The length of AC.
Solution:
It is given that B is the midpoint of line AC. So,
[tex]AB=BC[/tex]
[tex]6Y-14=10-2Y[/tex]
[tex]6Y+2Y=10+14[/tex]
[tex]8Y=24[/tex]
Divide both sides by 8.
[tex]Y=\dfrac{24}{8}[/tex]
[tex]Y=3[/tex]
The value of Y is 3.
Now,
[tex]AC=AB+BC[/tex]
[tex]AC=6Y-14+10-2Y[/tex]
[tex]AC=4Y-4[/tex]
Putting [tex]Y=3[/tex], we get
[tex]AC=4(3)-4[/tex]
[tex]AC=12-4[/tex]
[tex]AC=8[/tex]
Therefore, the length of AC is 8 units.
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