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If AB=k+3, BC=2k and AC=4kтИТ5, then for what value of 'k' does B lie on AC?
3
8
2
5
8
Since B lies on AC, the sum of the segments AB and BC must equal the whole segment AC. Simply equate the linear expressions: (k+3)+2k=4kтИТ5.
AB = k + 3, BC = 2k, AC = 4k - 5. Point B lies on line segment AC.
AB+BC=AC
Since B lies on AC, the sum of the segments AB and BC must equal the whole segment AC. Simply equate the linear expressions: (k+3)+2k=4kтИТ5.
Assuming AC is the longest side and mistakenly setting AB + AC = BC or BC + AC = AB; the condition 'B lies on AC' implies B is between A and C, meaning AB + BC = AC.
Set up the equation
If point B lies on line segment AC, then the sum of the lengths of the two parts AB and BC must equal the total length of segment AC.
AB+BC=AC
Substitute the given values
Plug the expressions for AB, BC, and AC into the equation.
(k+3)+2k=4kтИТ5
Simplify the equation
Combine the like terms on the left side: (k+2k)+3=3k+3.
3k+3=4kтИТ5
Solve for k
Subtract 3k from both sides and add 5 to both sides to isolate k.
3+5=4kтИТ3kтЯ╣k=8
B is correct because solving the equation (k+3)+2k=4kтИТ5 yields k=8.
This concept of segment addition is foundational for coordinate geometry and vector addition where points satisfy A+AB=B.
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