# Thread: Finding a point on a line

1. ## Finding a point on a line

So the formula for finding it has been explained to me as thus:

BD/DA=CE/EA

I understand the basis for this formula, what I struggle with is the item identification. So in the case of A=(-10,-4), and C= (8,5), find the y coordinate for B when x=-1. The example I'm given is as so

BD/(-1-(-10))=(5-(-4))/(8-(-10)), or more cleanly BD/9=9/18

It then breaks down to BD=9/2, which I understand. It then tells me since the B is higher than D (which makes 0 sense to me), that B is the y coord of D plus the length of BD, therefore -4+(9/2) (or 1/2).

Can someone help explain the item identification and the last part of why B is D+BD?

2. ## Re: Finding a point on a line

Originally Posted by Tyro
So the formula for finding it has been explained to me as thus:

BD/DA=CE/EA

I understand the basis for this formula, what I struggle with is the item identification. So in the case of A=(-10,-4), and C= (8,5), find the y coordinate for B when x=-1. The example I'm given is as so

BD/(-1-(-10))=(5-(-4))/(8-(-10)), or more cleanly BD/9=9/18

It then breaks down to BD=9/2, which I understand. It then tells me since the B is higher than D (which makes 0 sense to me), that B is the y coord of D plus the length of BD, therefore -4+(9/2) (or 1/2).

Can someone help explain the item identification and the last part of why B is D+BD?
Please state the question exactly as given to you. Please do not try to give your interpretation. Frankly what you posted is meaningless.

3. ## Re: Finding a point on a line

You'll need to provide more context about this "formula" ... frankly, I don't know what you're saying.

For your problem, I would do it as follows ...

The equation for line AC in slope-intercept form {recall ... $y-y_1 = m(x-x_1)$} is

$y - 5 = \dfrac{5-(-4)}{8-(-10)}(x - 8)$

$y - 5 = \dfrac{1}{2}(x - 8)$

$x = -1 \implies y-5 = -\dfrac{9}{2} \implies y = \dfrac{1}{2}$

4. ## Re: Finding a point on a line

The questions was stated exactly as it was given to me. The point A (-10,-4), and the point C (8,5) are 2 points on a line. Find the y coordinate for B (-1,y) (B is also on the same line)

5. ## Re: Finding a point on a line

Originally Posted by Tyro
The questions was stated exactly as it was given to me. The point A (-10,-4), and the point C (8,5) are 2 points on a line. Find the y coordinate for B (-1,y) (B is also on the same line)
Well, the solution is given in my previous post ... only "formula" necessary is the point-slope form for finding the linear equation between two given points on the plane.

6. ## Re: Finding a point on a line

So to apply your formula to another equation so I can make sure I understand,

A=(-7, -10) C=(10,-1), B= (2, y)

I'd go y-(-1)=(9/17)(-8)
y+1=-72/17
y=-89/17?

7. ## Re: Finding a point on a line

Originally Posted by Tyro
So to apply your formula to another equation so I can make sure I understand,

A=(-7, -10) C=(10,-1), B= (2, y)

I'd go y-(-1)=(9/17)(-8)
y+1=-72/17
y=-89/17?
that will work ...

8. ## Re: Finding a point on a line

Originally Posted by Tyro
The questions was stated exactly as it was given to me. The point A (-10,-4), and the point C (8,5) are 2 points on a line. Find the y coordinate for B (-1,y) (B is also on the same line)
Originally Posted by skeeter
Well, the solution is given in my previous post ... only "formula" necessary is the point-slope form for finding the linear equation between two given points on the plane.
It is sufficient to use the slope formula. Line segments AB, BC, and AC all lie on the same line and have the same slope. Pick any pair of slopes among the line segments AB, BC, and AC.

Calculate the two slopes and set them equal to each other. You'll be guaranteed that there will be at least one y-variable in the equation. Solve for y.

I have decided to work the slopes of line segment AB and line segment AC:

$\dfrac{y - (-4)}{-1 - (-10)} \ = \ \dfrac{5 - (-4)}{8 - (-10)}$

$\dfrac{y + 4}{-1 + 10} \ = \ \dfrac{5 + 4}{8 + 10}$

$\dfrac{y + 4}{9} \ = \ \dfrac{9}{18}$

$\dfrac{y + 4}{9} \ = \ \dfrac{1}{2}$

$2(y + 4) \ = \ 9(1)$

$2y + 8 \ = \ 9$

$2y \ = \ 1$

$y \ = \ \dfrac{1}{2}$