Question

31. MODELING WITH MATHEMATICS

Your school lies directly between your house and the movie theater. The distance from your house to the school is one-fourth of the distance from the school to the movie theater. What point on the graph represents your school?​

Answer 1

(-2.2, -1.2) on the graph represents your school.

Explanation:

By the given figure,

The point that represents the house = (-4, -2), ( let H )

And, the point that represents the theater = (5, 2) ( let T )

Suppose S represents the point that shows the school,

According to the question,

S is between the line segment HT such that the distance from H to the S is one-fourth of the distance from S to the T,

i.e. the point S divides the segment HT into the ratio 1 : 4 internally,

By the segment formula,

The coordinates of point S,

`((1* 5+4* -4)/(1+4), (1* 2+4* -2)/(1+4))`

`=((5-16)/(5), (2-8)/(5))`

`=((-11)/(5), (-6)/(5))`

`=(-2.2, -1.2)`

Hence, (-2.2, -1.2) on the graph represents your school.