Answer to Question #163093 in Geometry for azura

Question

A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?

Answer 1

The equation of line passing through A and B is given as:

-7x + 3y = -21.5

Or

3y = 7x -21.5

Or

y = (7/3)x -7.16

Also, At x = 0, y = -7.16, Therefore, point A = (0, -7.16)

And At y = 0, x = 3, Therefore, point B = (3, 0)

The center point of AB is (0+3/2, -7.16+0/2) = (1.5, -3.58)

On comparing with y = mx + c

The slope is m = (7/3)

The line passing through the center of AB will be perpendicular to line AB.

Therefore, the slope of the line perpendicular to AB is given by:

m2 = -1/m = -3/7

Therefore, the line passing through (1.5, -3.58) with slope = 3/7 is given by:

y = mx + c

y = (3/7)x + c

the line passes through (1.5, -.358), Therefore,

-3.58 = (3/7)*1.5 + c

Or c = -3.58 - 0.64 = -4.22

Therefore, the line passing through (1.5, -3.58) with slope = 3/7 is given by:

y = mx + c

y = (3/7)x - 4.22

Or

7y = 3x - 29.5

Or

3x - 7y - 29.5 = 0

Final Answer:

3x - 7y - 29.5