If point [tex]$P$[/tex] is [tex]$\frac{4}{7}$[/tex] of the distance from [tex]$M$[/tex] to [tex]$N$[/tex], what ratio does the point [tex]$P$[/tex] partition the directed line segment from [tex]$M$[/tex] to [tex]$N$[/tex] into?
A. 4:1
B. 4:3
C. 4:7
D. 4:10
Answer (2)
The final answer is 4 : 3
Examples
In architecture, when designing a structure, you might need to divide a beam into specific ratios to support different loads. If a support point P needs to be placed 4/7 of the way along a beam MN, this calculation ensures the beam is divided in a 4:3 ratio, optimizing weight distribution and structural integrity.
Point P partitions the directed line segment from M to N in the ratio 4 : 3 . This is determined by calculating the lengths of segments MP and PN , where MP is 7 4 of MN and PN is 7 3 of MN . Thus, the correct answer is option B: 4:3.
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