Can some one please explain to me how to do this???
You are walking across a field to get to a hiking path. Use the graph below to find the shortest distance you can walk to reach the path. Explain how you know you have the shortest distance.
In the graph, the point where you are at is (60,100)
the path forms a line connected by two lines,
(25,10) and (50,0)
the x axis goes by 10's and the y axis goes up by 20's.
from where you are, draw a perpendicular to the line.
Okay... I did, now where should I go from here?
If P(p,q) is a point not on the line
Ax + By + C = 0 , then the shortest distance from P to the line is
|Ap + Bq + C|/√(A^2 + B^2)
so find the equation of the line in the above form, then apply the formula
To find the shortest distance from your current point (60, 100) to the hiking path, you can use the concept of distance formula. The distance formula calculates the shortest distance between two points on a coordinate plane.
The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) represents the coordinates of your starting point, and (x2, y2) represents the coordinates of your destination point.
In this case, your starting point is (60, 100), and the hiking path is formed by the points (25, 10) and (50, 0).
1. Calculate the distance from your starting point (60, 100) to the first point on the path (25, 10):
d1 = √((25 - 60)^2 + (10 - 100)^2)
= √(( -35)^2 + (-90)^2)
≈ √(1225 + 8100)
≈ √9325
≈ 96.5
2. Calculate the distance from your starting point (60, 100) to the second point on the path (50, 0):
d2 = √((50 - 60)^2 + (0 - 100)^2)
= √((-10)^2 + (-100)^2)
≈ √(100 + 10000)
≈ √10100
≈ 100.5
3. Compare the distances obtained in steps 1 and 2. The shortest distance you can walk to reach the path is the smaller of the two distances.
In this case, the shortest distance is approximately 96.5 units, which is the distance from your starting point to the first point on the path (25, 10). This means that if you walk directly towards this point, you will cover the shortest distance to reach the hiking path.
Therefore, by using the distance formula and comparing the distances, you can determine the shortest distance to walk from your current position to reach the hiking path.