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Point location - Calculate the Center Between the Two End-Points

by Mark
(USA)

Graph Showing End Points

Graph Showing End Points













































Hello:
Can anyone point me to the math needed / equation to find the X and Y point on the imaginary line between the two arc end-points "x's" when a point on the arc is projected straight down vertically.
The "X" value point is "x" value from a point on the arc.
I need to find the "Y" value.

I know the values of the end-points and ONE point in the middle of the two endpoints that establishes the height of the arc.
I know how to calculate the center between the two end-points.
Thanks in advance.
Mark

Comments for Point location - Calculate the Center Between the Two End-Points

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Jul 17, 2011
Calculate the Center Between the Two End-Points
by: Staff


The question:

by Mark
(USA)


Hello:

Can anyone point me to the math needed / equation to find the X and Y point on the imaginary line between the two arc end-points "x's" when a point on the arc is projected straight down vertically.

The "X" value point is "x" value from a point on the arc.
I need to find the "Y" value.

I know the values of the end-points and ONE point in the middle of the two endpoints that establishes the height of the arc.

I know how to calculate the center between the two end-points.
Thanks in advance.

Mark


The answer:


I’m unclear on exactly what you are asking.

If you want to find the x or y value of a point on an imaginary straight line exactly midpoint between two known “x” points shown on the graph, this can be computed as follows:


The coordinates of the “first x” are: (x₁,y₁)
The coordinates of the “second x” are: (x₂,y₂)

Coordinates of the point exactly half way in between= [(x₁+x₂)/2),(y₁+y₂)/2]





The equation for a straight line passing through two known points is shown below:


since you know the coordinates of the two points, you can calculate the slope (m)of the straight line which passes through both points as follows:

m = (y₂ - y₁)/(x₂ - x₁)


The slope-intercept form of an equation connecting the two points is:

y = mx + b

m = slope of line
b = y intercept

x & y are the x and y coordinates of any point on the straight line.

Once you know the slope of the line, you can solve for the y-intercept (b), and you are finished.

Here is an example:

Suppose you wish to write an equation for a straight line passing through the following two points: (5,12) and (10, 15)

The slope of a straight line passing through both points is:

m = (y₂ - y₁)/(x₂ - x₁)
m = (15 - 12)/(10 - 5)
m = 3/5

The equation for the straight line itself is:

y = mx + b
y = (3/5)*x + b

Solve for “b” using the coordinates of either of the known points:

The coordinates of the first known point are: (5,12)

y = (3/5)*x + b

12 = (3/5)*5 + b

12 = 3*(5/5) + b

12 = 3*(1) + b

12 = 3 + b

12 - 3 = 3 - 3 + b

9 = 0 + b

9 = b


The final equation for the straight line is:

y = (3/5)*x + 9







Thanks for writing.

Staff
www.solving-math-problems.com



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