# Answer in Geometry for gfjbhjl #217221

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 -7*x* + 3*y* = -21.5. What is the equation of the central street *PQ*?

Solution.

The equation of the line passing through *A* and *B* is: “-7x + 3y = -21.5.”

It can be written as: “y=frac{7}{3}xu200bu2212frac{21.5}{3}.nu200b”

By comparing with the standard form “y=mx+c,” the slope of this line is “m=frac{7}{3}.”

Central street PQ is perpendicular to the line passing through *A *and *B. *Product of slopes of perpendicular lines is “m1*m2=-1”.

Slope of the perpendicular line is:“Slope; of ;perpendicular; line=newline = frac{-1}{slope;of;parallel;line}=frac{-1}{frac{7}{3}}=frac{-3}{;7}.”

Thus the equation of line is: “y=mx+c; newlineny=frac{-3}{7}x+c; newlinen7y= -3x+7c; newlinen7y+3x=7c.”

Dividing by *2:*

“3.5y+1.5x=3.5c.”

To find *c *with just this information is impossible.It is needed to check the options of the line with the slope -3/7

on the figure.

The line *PQ *passes through the point (7,6) on the figure.Hence the equation of the line can be found out, using point slope form of a line: “yu2212y_1=m(xu2212x_1).”

Slope is “frac{-3}{7}” .

“(x_1,y_1) ;is; (7,6).”

“y-6=frac{-3}{7}(x-7); newlinen7(y-6)=-3(x-7); newlinen7y-42=-3x+21; newlinen7y+3x=21+42; newlinen7y+3x=63.”

This is the equation of the central line.

Dividing by 2:

“3.5y+1.5x=31.5.”

Or

“-3.5y-1.5x=-31.5” is also the equation.

Answer:

“3.5y+1.5x=31.5”

or

“-3.5y-1.5x=-31.5”.