Junior cert Maths question

gra26

Hi,

Can someone point me in the direction of a proof that for two perpendicular lines with slopes m1 an m2 that m1m2=-1 that is suitable for a junior cert student.

I can prove it using a few different methods but I want one that's suitable for that particular level and I'm not sure which one might be suitable.

Thanks

ray giraffe

I could be wrong but I don't think Junior certs need to be able to prove it!

Also I think a proof would be too difficult for any Junior Cert to appreciate.

I think drawing two perpendicular lines on graph paper, measuring their slopes and multiplying the answers to give -1 should be enough justification.

Attached is a simple proof, however only an Honours Leaving Cert student would really appreciate it.

MathsManiac

That's a nice straightforward proof, Ray, and I think that a lot of JCHL students would be able to follow/appreciate it, especially if it was preceded by some suitable preliminary work with Geogebra or similar.

It's certainly no harder than some of the geometry proofs that they are supposed to be able to do.

Suppose you had previously done some visual work so that they already appreciated that, when the "run" is 1, then the "rise" is the slope. Then they should be able to see the significance of the a and b straight away.

Also, the ratio relationship can be seen as coming from tan(theta) either, if they have difficulty with the similar triangles.

Perhaps another way of approaching a proof might be to consider a "slope diagram" showing a slope of a/b, and then show a second version rotated 90 degrees clockwise, giving a slope of -b/a. It's clear from there that the product is -1.

Perp_slopes.GIF

gra26

That's great. Thanks both of you.

ray giraffe

MathsManiac wrote: »

consider a "slope diagram" showing a slope of a/b, and then show a second version rotated 90 degrees clockwise, giving a slope of -b/a. It's clear from there that the product is -1.

Yes! I think this is great for Junior Cert



Just explain that one triangle is rotated 90 degrees from the other one

That's straight from the Book!

gra26

What about tan(90) is undefined and since tan(theta)=m1+m2/1+m1m2 then 1+m1m2=0?

Though I do like the ones involving the two triangles.

ray giraffe

Yes gra, that proof is fine - but that formula is not done for Junior Cert!

gra26

Ok. Triangles it is. Thanks!