What is the explanation for 2(xo)(yo) = 2?

[TheKracken]

Homework Statement

we had a a function on a graph of f(x)=1/x and then we are suposed to find the area of a triangle where the tangent line is the hypontenuse, and the x and y-axis are the base and hight...i found f'(x)= -1/x^2
from here i used the formula y-yo=x0(x-x0) and got that the x intercept is 2xo and then got the y intercept to be 2yo which means those are the lengths of the base and the hight, from there you use the formula of a triangle and that is (2)(2)(xo)(yo) all over 2 and then i canceled out the 2's and got 2(xo)(yo) as the area of the triangle...and this all is correct...but how the heck does the also = 2? apperantly 2(Xo)(Yo)=2...could someone please explain this, possibly just some basic algebra rule and I'm having a brain fart?



by the way, this is off of MIT's OCW...

 

[SammyS]

Homework Statement

we had a a function on a graph of f(x)=1/x and then we are suposed to find the area of a triangle where the tangent line is the hypontenuse, and the x and y-axis are the base and hight...i found f'(x)= -1/x^2
from here i used the formula y-yo=x0(x-x0) and got that the x intercept is 2xo and then got the y intercept to be 2yo which means those are the lengths of the base and the hight, from there you use the formula of a triangle and that is (2)(2)(xo)(yo) all over 2 and then i canceled out the 2's and got 2(xo)(yo) as the area of the triangle...and this all is correct...but how the heck does the also = 2? apperantly 2(Xo)(Yo)=2...could someone please explain this, possibly just some basic algebra rule and I'm having a brain fart?

by the way, this is off of MIT's OCW...

What is y₀ in terms of x₀ ?

After all, isn't y₀ = f(x₀) ?

 

[TheKracken]

What is y₀ in terms of x₀ ?

After all, isn't y₀ = f(x₀) ?

yes...but I don't think that makes a difference...you still need some form of units don't you? because if the answer is 2...then its 2 what? 2 inches? 2 meters? I understood it all the way up until he said therefor it =2

 

[SammyS]

The units will cancel.The units of y are the reciprocal of the units of x.The units of area for this graph are units of x times units of y.

 

[TheKracken]

So I wouldn't be wrong if I left the units then would I? Or is it best to cancle and simplify like that?

 

[SammyS]

So I wouldn't be wrong ifg I let the units then would I? Or is it best to cancel and simplify like that?

The sentence doesn't make sense. Is there a typo ?

 

[TheKracken]

sorry, yes there was some typos...fixed

 

[SammyS]

So I wouldn't be wrong if I left the units then would I? Or is it best to cancel and simplify like that?

Whatever the units for x, the area of the triangle will not have units. It's a pure number.

 

[TheKracken]

Whatever the units for x, the area of the triangle will not have units. It's a pure number.

Alright...now that I am thinking about it I think I understand...its because the x's arnt labeled with a unit/number.