Question

A community recently converted an old railroad corridor into a recreational trail. The graph at the right shows a map of the trail on a coordinate grid. The community plans to construct a path to connect the trail to a parking lot. The new path will be perpendicular to the recreational trail.A. Write an equation of the line representing the new path. B. What are the coordinates of the point at which the path will meet the recreational trail?

Answer 1

The equation of a line is represented by the equation y = mx+c where

m is the slope

c is the intercept

Slope of the line = y2-y1/x2-x1

slope of the line = 150-0/150-75

slope of te line = 150/75

slope of the line = 2

intercept is a point where the line cuts the y axis

The new path cuts the y axis at 100. Hence c = 100

The equation becomes y = 2x=100

2) The coordinates of the point where the path will meet recreational line is arounsd (80, 20) on the graph. THe line will cut the rereational line at this coordinates to make it perpendicular to the line recreation