Question

1. your school lies directly between your home and the movie theater. the distance from your home to the school is one - fourth of the distance from the school to the movie theater. what point on

Explanation:

Step1: Let the distance from home to school be $x$ and from school to movie - theater be $y$.

Given $x=\frac{1}{4}y$.

Step2: Consider the total distance from home to movie - theater as $D=x + y$.

Substitute $x=\frac{1}{4}y$ into $D$, we get $D=\frac{1}{4}y+y=\frac{1 + 4}{4}y=\frac{5}{4}y$.

Step3: Find the fraction of the distance from home to school in terms of the total distance.

The fraction is $\frac{x}{D}$. Since $x=\frac{1}{4}y$ and $D = \frac{5}{4}y$, then $\frac{x}{D}=\frac{\frac{1}{4}y}{\frac{5}{4}y}=\frac{1}{5}$.

Answer:

The point that represents the school is $\frac{1}{5}$ of the way from home to the movie - theater.