SOLUTION: A road is to be constructed perpendicular to an established road. A surveyor determines that the original road passes through the points (4,9) and (2,13). The roads must intersect

Question 252782: A road is to be constructed perpendicular to an established road. A surveyor determines that the original road passes through the points (4,9) and (2,13). The roads must intersect at (4,9) Write the equation of the second road.
Found 3 solutions by rapaljer, checkley77, JimboP1977:
Answer by rapaljer(4671)   (Show Source): You can put this solution on YOUR website!
The slope of the established road is .

The slope of the perpendicular road is the negative reciprocal = 1/2. If it passes through the point (4,9), then you would probably want to use the point slope formula:
y-9=1/2(x-4)
y-9=1/2x-2

Add +9 to each side:
y=1/2x-2+9
y=1/2x+7

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Answer by checkley77(12844)   (Show Source): You can put this solution on YOUR website!
I always thought perpendicular meant at right angles rather than parallel?
First road slope:
Slope=(13-9)/(2-4)=4/-2=-2
Equation for the original road:
y=-2x+9 (red line)
Parallel road slope=-2
Y=mX+b
9=-2*4+b
9=-8+b
b=9+8
b=17 is the Y intercept of the parallel road.
Equation for the pasrallel road. (green line)
(graph 300x200 pixels, x from -6 to 10, y from -10 to 20, of TWO functions -2x +9 and -2x +17).

Answer by JimboP1977(311)   (Show Source): You can put this solution on YOUR website!

RELATED QUESTIONS
Q: A road constrution company has been constructed to build the road with grad of 12... (answered by Alan3354)
Smith Engineering is in the process of reviewing the salaries of their surveyors. During... (answered by josmiceli)
A road is tangent to a circular lake. Along the road and 12 miles from the point of... (answered by Alan3354)
A road is tangent to a circular lake. Along the road and 12 miles from the point of... (answered by greenestamps)
Alice walks along a road which can be modeled by the equation y=6x, where (0,0)... (answered by greenestamps)
The town of Foxton lies 10 mi north of an abandoned east-west road that runs through... (answered by ankor@dixie-net.com)
The town of Foxton lies 10 mi north of an abandoned east-west road that runs through... (answered by ankor@dixie-net.com)
Clara cycles at a constant speed of 8 meters per second from west to east along a path.... (answered by ikleyn)
smith engineering is in the process of reviewing the salaries of their surveyors. during... (answered by DrBeeee)