Question

The X and Y coordinates (in feet) of station Shore are 5048.64 and 3278.59, respectively, and those for station Rock are 3033.33 and 5876.93, respectively. Suppose a point P is located near the straight line connecting stations Shore and Rock. What is the perpendicular distance from P to the line if the X and Y coordinates of point P are 4433 22 and 4242.37, respectively?

Answer 1

To find the perpendicular distance from point P to the line connecting stations Shore and Rock, we can use the distance formula. We can calculate the coefficients of the equation of the line using the coordinates of stations Shore and Rock, and then plug in the coordinates of point P to find the distance.

Step-by-step explanation:

To find the perpendicular distance from point P to the line connecting stations Shore and Rock, we can use the formula for the distance between a point and a line. The formula is:

Distance = | (A*xP + B*yP + C) / sqrt(A2 + B2) |

Where A, B, and C are the coefficients of the equation of the line. In this case, the equation of the line is Ax + By + C = 0. We can find the values of A, B, and C using the coordinates of stations Shore and Rock. Plugging in the values, we get:

A = 5876.93 - 3278.59 = 2598.34

B = 3033.33 - 5048.64 = -2015.31

C = -A * 5048.64 - B * 3278.59

Plugging in the coordinates of point P, we get:

xP = 4433.22

yP = 4242.37

Using these values, we can calculate the perpendicular distance from P to the line.