Question

A directed line segment on a gridded map shows the path of a hot air balloon from 1(0,0) to B(8,4). Each grid unit represents 1 mile. The balloon traveled at a constant speed of 20 miles per hour Point V divides line segment AB in the ratio 6 to 2.
a) What are the coordinates of point V? Round to the nearest tenth if necessary


b) Mary states that the distance from point A to point Vis 6 miles. What is Mary's mistake? What is the

correct distance? (Check)

Answer 1

Answer:

Step-by-step explanation:

There is  a point V with ration 6 to 2, therefore we must find the coordinates of point V and the distance from A to V

According to the graph

$c^{2}=x^{2}+y^{2}\\c^{2}=8^{2}+4^{2}\\c=\sqrt{64+16}=8.9.4\\sin\alpha =\frac{4}{8.94}$

α≅27°

V=2*8.94/6 (ratio 6:2)

V=2.98mile

$sin27=\frac{y}{2.98}\\y=sin27*2.98=1.35\\cos27=\frac{x}{2.98}\\x=cos27*2.98=2.65$

coordinates of V = (2,65;1.35)

Distance from A to V

$d_{AV}=2.98 miles$

finally

Mary's mistake is to take the 6 to 2 ratio as the distance traveled from the globe only in the x direction