College Algebra(Perpendicular lines)

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?

guardgirl08 said:

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).

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Suppose that \(\displaystyle m\) is the slope determined by \(\displaystyle (1,2)~\&~(-2,-5)\).
Then the new slope will be \(\displaystyle \frac{-1}{m}\).

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.

Re:

mmm4444bot & lookagain edit said:

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.

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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.

Re:

mmm4444bot said:

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.

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

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

Re:

mmm4444bot said:

lookagain said:

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

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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 !



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

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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