Question

a line is drawn through point (1,2) forming a right triangle with the positive x- and y-axes. The slope of the line forming the triangle of least area is...

Answer 1

got anything??

Answer 2

not yet lol

Answer 3

haha okay

Answer 4

but im making dinner for my kids and thinking it over

Answer 5

thanks!

Answer 6

are you expected to use calculus or vectors to solve this one?

Answer 7

calc

Answer 8

ok

Answer 9

its a question from my practice AP calc book

Answer 10

i know the answer, i just don't know how to get it

Answer 11

yeah, that's always the hard part hehe

Answer 12

always! haha

Answer 13

what part of calc are you in? multivariable, langrange multipliers or just single variable?

Answer 14

uhmm i'm in Calc AB..

Answer 15

ok

Answer 16

ok. Well the area of this right triangle is:\[A=\frac{1}{2}xy\]Now we need to relate x and y with one another. The line through the point (1,2) is our hypotenuse. It crosses the x axis at the point (0,y) and it crosses the y-axis at the point (x,0). The slope of this line is:\[m=\frac{y-2}{x-1}\]Taking the point (x,y)=(0,y) we get \[y=2-m\] where m is a constant. We have:\[A(x)=\frac{1}{2}(x)(2-m)\]Now we differentiate and set equal to zero to find the critical points:\[A'(x)=\frac{2-m}{2}=0\]so, m=2.

Answer 17

hmm. well my answer key says its supposed to be -2..

Answer 18

im missing something here. It makes sense that the slope is negative though since the triangle is bound by the x and y axes.

Answer 19

yeah, that's why i can't figure it out either lol

Answer 20

I know its a simple matter of a negative sign but I cant justify it!?!

Answer 21

sorry, if I figure it out later Ill let you know but too many distractions tonight!

Answer 22

alright, well thanks for trying! :)