Question

Fernando and Maria are at opposite sides of a park. They plan to meet later at a fountain that is located somewhere between them. Maria will arrive at the fountain first, before Fernando even leaves his starting location. The ratio of Maria's starting location to the fountain to Fernando's starting place is 5:3. What is the location of the fountain? Round to the nearest tenth, if necessary.

Answer 1

Answer:

(-1,-0.5)

Step-by-step explanation:

We can see from our given graph that Fernando is at point (-4,-2) and Maria is at point (4,2). They will meet at the fountain located somewhere between them.

We can see that fountain will divide our given line segment internally, so we will use section formula, when a point internally divides a segment in ratio m:n.

$[\frac{m*x_2+n*x_1}{m+n},\frac{m*y_2+n*y_1}{m+n}]$

Let location of Maria be point $(x_2,y_2)$ and location of Fernando be $(x_1,y_1)$.

Upon substituting m=3 and n=5 in section formula we will get,  

$[\frac{3*4+5*-4}{3+5},\frac{3*2+5*-2}{3+5}]$

$[\frac{12-20}{8},\frac{6-10}{8}]$

$[\frac{-8}{8},\frac{-4}{8}]$

$[-1,-0.5]$

Therefore, the fountain is located at point (-1,-0.5).

Answer 2

Answer:

-1 and -1/2

Step-by-step explanation: