subject
Mathematics, 22.06.2019 21:00 recon12759

What is the equation of the line that passes through (-2, 5) and is perpendicular to the line whose equation is y = 1/2x + 5?

Answers

ansver
Answer from: liyahheadhigh
Y=-0.5+4
The equation would be set up as 5y+-0.5(-2)+b reciprocal of 1/2 is 0.5 it’s negative because it’s perpendicular multiply 0.5 by -2 which is 1 subtract 1 from the 5y you have 4.
ansver
Answer from: Jana1517

let's keep in mind that perpendicular lines have negative reciprocal slopes, hmmmmm what's the slope of the line through (-6,1/2) and (-4,2/3) anyway?


\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{\frac{1}{2}})\qquad  (\stackrel{x_2}{-4}~,~\stackrel{y_2}{\frac{2}{3}}) \\\\\\ slope =  m\implies  \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{~~\frac{2}{3}-\frac{1}{2}~~}{-4-(-6)}\implies \cfrac{~~\frac{4-3}{6}~~}{-4+6} \\\\\\ \cfrac{~~\frac{1}{6}~~}{2}\implies \cfrac{~~\frac{1}{6}~~}{\frac{2}{1}}\implies \cfrac{1}{6}\cdot \cfrac{1}{2}\implies \boxed{\cfrac{1}{12} } \\\\[-0.35em] ~\dotfill


\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{12}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{12}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{12}{1}}\implies -12}


so we're really looking for the equation of a line whose slope is -12 and runs through -2,5.


\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})~\hspace{7em} slope =  m\implies -12 \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-5=-12[x-(-2)] \\\\\\ y-5=-12(x+2)\implies y-5=-12x-24\implies \blacktriangleright y=-12x-19 \blacktriangleleft

ansver
Answer from: zanaplen27
Here, if you have any questions feel free to ask
ansver
Answer from: chanelle16

Step-by-step explanation:

The given lines are perpendicular and as AB = AC , Therefore △ ABC is art . angled isosceles . Hence the line BC through ( 1 , 2) will make an angles of ±45

with the given lines . Its equations is y - 2 = m (x - 1) where m = 1 / 7 and -7 as in .Hence the possible equations are 7x + y - 9 = 0 and x - 7y + 13 = 0

Alt :

The two lines will be parallel to bisectors of angle between given lines and they pass through ( 1, 2)

∴ y - 2 = m ( x - 1)

where m is slope of any of bisectors given by

5

3x+4y−5

5

4x−3y−15

or x - 7y + 13 = 0 or 7x + y - 20 = 0

∴ m = 1 / 7 or - 7

putting in (1) , the required lines are 7x + y - 9 = 0

and x - 7y + 13 = 0 as found above

Other questions on the subject: Mathematics

image
Mathematics, 20.06.2019 18:04, alyssa0888
In a basketball drill two players start at the same spot on the court. one player runs 6feet down the court and the other player runs 4.5 feet across the court (in a direction perpendicular to the first player l) what is the distance that one player must pass the ball for it to reach the other
Answers: 3
image
Mathematics, 21.06.2019 13:10, weirdest16
In the surface area formula for cylinders which expressionrepresents the lateral area
Answers: 1
image
Mathematics, 21.06.2019 16:20, zay65307
Two positive integers are 3 units apart on a number line. their product is 108. which equation can be used to solve for m, the greater integer? m(m – 3) = 108 m(m + 3) = 108 (m + 3)(m – 3) = 108 (m – 12)(m – 9) = 108
Answers: 1
image
Mathematics, 21.06.2019 18:30, Jenniferwolf
Ametal rod needs to be 9 feet and 5.5 inches in length. the sections of the poles being used are each 1 foot and 10.5 inches long. how many 1ft 10.5in sections would be needed to complete the 9ft 5.5in metal rod? and how many inches of material will be left?
Answers: 1
You know the right answer?
What is the equation of the line that passes through (-2, 5) and is perpendicular to the line whose...

Questions in other subjects:

Konu
Social Studies, 10.02.2021 01:50
Konu
Geography, 10.02.2021 01:50
Konu
Mathematics, 10.02.2021 01:50
Questions on the website: 13535161