Answer:
The point where he buried his treasure is (9.04,10.74)
Explanation:
First of all, we are going to find the equation of the line which describes the first path crossed by the horseman. In order to find it we have to take in account that the vector V provides us the direction of this path. We can associate the direction with the slope of the line. The slope is defined by the ratio of the vertical changes to horizontal changes between two points.
According to the V=6i+5j we can determine that:
Vertical change (y)= 5
Horizontal change (x)=6
Slope=\frac{5}{6}
Now , using the point- slope form
The chosen point is the point where the horseman began riding (2,5). Therefore:
m=5/6
y1=5
x1=2
y-5=5/6(x-2)
y=
Since the horseman at some point turned at a right angle towards village B and he unchanged his direction until arrived in the village B, the second path must be described by a line perpendicular to the first path.
We should know that two lines are perpendicular if and only if their slopes are negative reciprocals This means m1*m2=-1
m1=5/6
m2=
In order to find the equation of the second path , we will use again the point-slope form.
The chosen point is the point where is located the Village B (8,12)
The coordinates of the point where the horseman buried a jar full of silver coins corresponds to the intersection of the path 1 and the path 2. Therefore we are going to equal the two equations of each path.
Solving this equality for x
X=8.98
Replacing this value in any of equations of the paths
y=10.74.
Finally, the point where he buried his treasure is (9.04,10.74)