Hayyleeyn1234idn
Answered

IDNLearn.com makes it easy to find accurate answers to your specific questions. Our platform provides trustworthy answers to help you make informed decisions quickly and easily.

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?

See attachment below for picture/answer choices

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 L class=

Sagot :

DarkAngelBabyidn
its B -1.5x − 3.5y = -31.5
Calculistaidn

Answer:

[tex]-1.5x-3.5y=-31.5[/tex]

Step-by-step explanation:

we know that

If two lines are perpendicular

then

the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

In this problem line AB and line PQ are perpendicular

Step 1

Find the slope of the line AB

The equation of the line AB is

[tex]-7x+3y=-21.5[/tex]

isolate the variable y

[tex]3y=7x-21.5[/tex] ------> [tex]y=(7/3)x-21.5/3[/tex]

The slope of the line AB is equal to

[tex]m1=7/3[/tex]

Step 2

Find the slope of the line PQ

remember that

[tex]m1*m2=-1[/tex]

we have

[tex]m1=7/3[/tex] ----> slope line AB

so

substitute and solve for m2

[tex](7/3)*m2=-1[/tex]

[tex]m2=-3/7[/tex]

Step 3

Find the equation of the line PQ

The equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-3/7[/tex]

[tex]P(7,6)[/tex]

substitute

[tex]y-6=(-3/7)(x-7)[/tex]

[tex]y=(-3/7)x+3+6[/tex]

[tex]y=(-3/7)x+9[/tex] -----> multiply by [tex]7[/tex] both sides

[tex]7y=-3x+63[/tex]

[tex]7y+3x=63[/tex] -----> divide by [tex]2[/tex] both sides

[tex]1.5x+3.5y=31.5[/tex] -----> multiply by [tex]-1[/tex] both sides

[tex]-1.5x-3.5y=-31.5[/tex]

We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.