Expressing q in Terms of a_1,b_1,a_2,b_2

[dirk_mec1]

Homework Statement

A tangent line at point A with coordinate (a,f(a)) of function f(x) intersects f(x) at point B coordinate (b,f(b)) . A vertical line is drawn from point p (a<p<b) and intersects f(x) at C. From C a perpendicular line to the tangent line is drawn which intersect the tangent line at point D with coordinate (q,f(q))

The tangent line can be described by $y_1(x) =a_1 x+ b_1$

|CD| can be described by $y_2(x) =a_2 x+ b_2$

Express q in terms of $a_1,b_1,a_2,b_2$

http://imageshack.us/photo/my-images/706/5cqg.jpg/

Homework Equations

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The Attempt at a Solution

I can find $a_1,b_1,a_2,b_2$ in terms of a, b, f(a) and f(b).

I can express q in terms of the slope of the tangent:

$$q = p + H \sin(\alpha) \cos(\alpha)$$

with
$$\alpha = arctan\left( \frac{f(b)-f(a)}{b-a} \right)$$

$$H = f(p) -y_1(p)$$
and now what?

 

[Mandelbroth]

Homework Statement

A tangent line at point A with coordinate (a,f(a)) of function f(x) intersects f(x) at point B coordinate (b,f(b)) . A vertical line is drawn from point p (a<p<b) and intersects f(x) at C. From C a perpendicular line to the tangent line is drawn which intersect the tangent line at point D with coordinate (q,f(q))

The tangent line can be described by $y_1(x) =a_1 x+ b_1$

|CD| can be described by $y_2(x) =a_2 x+ b_2$

Express q in terms of $a_1,b_1,a_2,b_2$

http://imageshack.us/photo/my-images/706/5cqg.jpg/

Homework Equations

-

The Attempt at a Solution

I can find $a_1,b_1,a_2,b_2$ in terms of a, b, f(a) and f(b).

I can express q in terms of the slope of the tangent:

$$q = p + H \sin(\alpha) \cos(\alpha)$$

with
$$\alpha = arctan\left( \frac{f(b)-f(a)}{b-a} \right)$$

$$H = f(p) -y_1(p)$$
and now what?

This is a fun Euclidean geometry problem.

$a_1q+b_1=a_2q+b_2$. Solve for $q$.

 

[verty]

I wonder if there is a mistake in this question. Expressing q in terms of $a_1$, $a_2$, $a_3$ and $a_4$ means we don't need to know what those numbers are.

 

[dirk_mec1]

This is a fun Euclidean geometry problem.

$a_1q+b_1=a_2q+b_2$. Solve for $q$.

I can seriously hit myself against the wall. Thanks man.

 

[Mandelbroth]

I can seriously hit myself against the wall. Thanks man.

No problem. They threw a lot of unnecessary information out there. It took me a minute too.