Question

1. in the diagram shown, m is the mid - point of lp and n is the mid - point of mp. which of the following is the ratio of np to lp? (1) 3 to 1 (2) 1 to 3 (3) 4 to 1 (4) 1 to 4

Explanation:

Step1: Define the mid - point relationship

Since $M$ is the mid - point of $\overline{LP}$, we have $LM = MP=\frac{1}{2}LP$.

Step2: Use the second mid - point

Since $N$ is the mid - point of $\overline{MP}$, we have $NP=\frac{1}{2}MP$.

Step3: Substitute $MP$ in terms of $LP$

Substitute $MP = \frac{1}{2}LP$ into the equation for $NP$. Then $NP=\frac{1}{2}\times\frac{1}{2}LP=\frac{1}{4}LP$.

Step4: Find the ratio

The ratio of $NP$ to $LP$ is $\frac{NP}{LP}=\frac{\frac{1}{4}LP}{LP}=\frac{1}{4}$, which means the ratio of $NP$ to $LP$ is $1$ to $4$.

Answer:

(4) 1 to 4