View Full Version : College Algebra(Perpendicular lines)

guardgirl08

06-14-2011, 12:59 PM

Given the points (1,2) and (-2,-5) find the equation of the line perpendicular to the line created between these two points and passing through the point (2,8).

Im not really sure where to start but I believe you would start by finding the slope of one of the lines?

If so after that you would plug it into the point-slope equation and find the slope intercept form?

Given the points (1,2) and (-2,-5) find the equation of the line perpendicular to the line created between these two points and passing through the point (2,8).

Suppose that m is the slope determined by (1,2)~\&~(-2,-5).

Then the new slope will be \frac{-1}{m}.

mmm4444bot

06-14-2011, 05:09 PM

you would start by finding the slope of one of the lines?

Yes. Find the slope of the line passing through the given pair of points. Knowing this slope allows you to calculate the slope that is perpendicular.

after that you would plug it into the point-slope equation

No. You substitute the new slope (calculated as shown by pka) into the Point-Slope form. Of course, you also substitute the coordinates of the given point through which the new line must pass.

If you were to use the same slope, you would end up with the equation for a parallel line, not perpendicular.

find the slope intercept form?

I supposed that Slope-Intercept is the form that most people would use to report their answer (although, after substituting the three numbers into the Point-Slope form, you have a valid equation for the perpendicular line). Does your assignment request the answer in a specific form?

Memorize these facts:

(1) Parallel lines have the same slope

(2) Perpendicular lines have slopes which are negative reciprocals of each other

The only exceptions are when one or more of the lines involved is vertical because vertical lines have no slope.

guardgirl08

06-15-2011, 02:43 PM

Thank you so much that was a lot of help.

And to answer your question it doesn't say it has to be in a specific form.

lookagain

06-16-2011, 01:00 AM

If you were to use the same slope, you would end up with the equation for a parallel line,

or the equation for the same line, depending on whether the point that the perpendicular

line lies on is not on the original line or is on the original line, respectively, but it will not

be perpendicular.

guardgirl08,

here is an example:

Given the points (0,0) and (5,5), find the equation of the line perpendicular to the line

created between these two points and passing through the point (2,2).

The equation of the line through the first pair of points is y = x, with m = 1.

However, if you wrongly use the original slope, m = 1, then you will get the same (identical) line,

y = x, which is not parallel to itself, as the point (2,2) lies on the same line that passes through

points (0, 0) and (5, 5).

One of the facts mentioned is that parallel lines have the same slope. Yes.

However, lines with the same slope are either parallel to each other, or they are the same line.

mmm4444bot

06-16-2011, 05:13 PM

it doesn't say it has to be in a specific form.

Then Slope-Intercept form should be fine.

MY EDIT: Deleted incorrect statement about point (2,8) lying on the first line.

lookagain

06-16-2011, 06:55 PM

Also, lookagain makes a good point. While typing my reply, I did not realize that the given point (2,8) lies on the first line.

Actually, (2, 8) does *not* lie on the original line, which is \ y \ = \ \frac{7}{3}x \ - \ \frac{1}{3}.

But I was considering the hypothetical of *if* (2, 8) had been on that original line.

mmm4444bot

06-16-2011, 07:22 PM

I was considering the hypothetical of *if* (2, 8) had been on that original line.

Oh, I get it now.

You inserted your hypothetical directly into a quotation of my words about the original exercise.

I think that faked me out !

:oops:

For my part, I should always complete exercises, before commenting on them. Perhaps, then, I might know more often what I'm talking about.

guardgirl08

06-19-2011, 10:03 AM

I was considering the hypothetical of *if* (2, 8) had been on that original line.

Oh, I get it now.

You inserted your hypothetical directly into a quotation of my words about the original exercise.

I think that faked me out !

:oops:

For my part, I should always complete exercises, before commenting on them. Perhaps, then, I might know more often what I'm talking about.

mmm4444bot,

Thank you for your help. Every little bit counts for me because math is my worst subject.

guardgirl08

Also...thanks to everyone that helped me. I love this site. Keep up the good work and I will be using you again when I need to(:

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