Asoftware 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?
a. -3x + 4y = 3
b.-1.5x − 3.5y = -31.5
c.2x + y = 20
d.-2.25x + y = -9.75

Option B is correct .i.e., -1.5x - 3.5y = -31.5

Step-by-step explanation:

Given: All streets are either parallel or perpendicular.

            Equation of Street AB , -7x + 3y = 21.5

To find Equation of Street PQ

Re write the given equation in form of slope and intercept form

we get,

From this slope of street AB is [tex\frac{7}{3}[/tex].

From given pic Street PQ is perpendicular to street AB.

we know that product of slope of perpendicular lines should be equal to -1

let slope of PQ = m

Slope of line in Option A).

Slope =

So, this is not required equation.

Slope of line in Option B).

Slope =

So, this is required equation.

Therefore, Option B is correct .i.e., -1.5x - 3.5y = -31.5

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.