how to determine one coordinate of a point that lies on a linethe line is determined by endpoints

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

You would like a method to determine one of the coordinates of a point that lies on a line defined by its end points.

Let the end points of the line be (x1, y1) and (x2, y2). The equation of the line is:

(y - y1) = (x - x1)*[(y2 - y1)/(x2 - x1)]

Let the point that lies on this line be (C , D) where D is unknown

We can substitute x and D in the equation of the line and solve for D

(D - y1) = (C - x1)*[(y2 - y1)/(x2 - x1)]

=> D = (C - x1)*[(y2 - y1)/(x2 - x1)] + y1

The value of the unknown coordinate can be determined using the formula obtained above.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll determine the equation of the line that passes through the points: (2,4) and (8,8)

(x2 - x1)/(x - x1) = (y2 - y1)/(y - y1)

We'll identify the cordinates:

x1 = 2, x2 = 8

y1 = 4, y2 = 8

We'll substitute into the formula:

(8-2)/(x - 2) = (8-4)/(y - 4)

6/(x-2) = 4/(y-4)

We'll cross multiply:

4(x-2) = 6(y-4)

We'll remove the brackets:

4x - 8 = 6y - 24

We'll add 24 both sides:

6y = 4x - 8 + 24

6y = 4x + 16

We'll divide by 6:

y = 2x/3 + 8/3

If the point (6,m) is on the line , then it's coordinates verify the equation of the line:

m = 2*6/3 + 8/3

m = 20/3

 

 

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