Hello, everybody. This sum is 4-th part of 6 parts in one sum. :confused: I just stopped here because I forgot formula.
I need to find altitude (h) CD and it length.

You are thinking of the distance from a point to a line formula.

Which is D=\frac{|Ax+By+C|}{\sqrt{A^{2}+B^{2}}}

First, find the equation of the line between (-3,3) and (9,-6).

We get y=\frac{-3}{4}x+\frac{3}{4}

In standard form so you can use the formula: 3x+4y-3=0

Now apply the formula to find the length h you have on your diagram. x=7 and y=8

To find the coordinates of the point. You have your line equation. Find the perpendicular bisector which passes through point (7,8).

Since it's perpendicular, the slope will be the negative reciprocal of the slope of the line we found. In other words, its slope will be 4/3.

8=\frac{4}{3}(7)+b

We find this perp. Bisector has equation y=\frac{4}{3}x-\frac{4}{3}

Set the two line equations equal and solve for x to find where they intersect. Then, y is easily found.

OK. How to make equation of h (CD) to AB, if I have AB=15, CD=10; C(7;8); D(x,y)?

The coordinates of point D are (1,0). We found those.

Now just use (7,8) and (1,0) to find the equation of the line. It's easy now.

Use y=mx+b. We found the slope m previously. You have an x and y. All you need to do is solve for b and you're done.

:) Hello! Thank you. You found the coordinates of point D - (1;0). :rolleyes: How did you do that? What formula did you use?

:) Next I solve:
CD=10,

CD:
x1=1,
y1=7,
x2=0,
y2=8.

x-1 y-7
---=---
0-1 8-7,

So, equation of CD must be x+y-8=0.
Is it correct?

I found the coordinates in the manner I outlined in my first post.

The line from (1,0) to (7,8) has equation y=\frac{4}{3}x-\frac{4}{3}

The other line has equation y=\frac{-3}{4}x+\frac{3}{4}

Set them equal and solve for x:

\frac{-3}{4}x+\frac{3}{4}=\frac{4}{3}x-\frac{4}{3}

:confused: I finally confused!!
OK Lets go again.

I have A(-3;3), B(9;-6), C(7;8) and I need to know D(x;y).

AB=15; 9x+12y-9=0; k=-3/4;
AC: 5x-10y+45=0; k=1/2;

next I have h=CD=10, and k=4/3 (how I understood), because k1*k2=-1

And I can't get how to calculate D(x;y). I can't see it's formula. Then it is easy to write equation of CD, what I need.

I outlined how to find it in my first post. You have the equation of the line from

(-3,3) to (9,-6). Now, the line which passes through point (7,8) and is perpendicular to this line will have slope which is the negative reciprocal of the line from (-3,3) to (9,-6).

Line equation from (-3,3) to (9,-6) is y=\frac{-3}{4}x+\frac{3}{4}

Therefore, the equation of the perpendicular line will have slope 4/3. You have a passing through point, (7,8), find the equation of the line. It is y=\frac{4}{3}x-\frac{4}{3}

Now, set them equal and solve for x. That is your point D so avidly sought. Then find y and you're done.

Look at my first post.