Welcome to class!
In today’s class, we will be talking about coordinate geometry of a straight line. Enjoy the class!
Coordinate Geometry of a Straight Line
Any straight line has an equation of the form
y = mx + c
where m, the gradient, is the height through which the line rises in one-unit step in the horizontal direction
c, the intercept, is the y-coordinate of the point of intersection between the line and the y-axis. This is shown in the figure below.
The straight line, y = mx + c
If we know the gradient m of a straight line with unknown intercept c, and the coordinates (x1 , y1) of a point through which it passes, then we know that
y1 = mx1 + c
c = y1 − mx1
If we substitute into
y = mx + c
y = mx− mx1 + y1
which we can rearrange to give
y− y1 = m(x − x1)
If we know two points (x1 , y1) and (x2 , y2) through which passes a line with unknown gradient m and intercept c, then
y1 = mx1 + c ,
y2 = mx2 + c
Subtracting the first equation from the second gives
y2 − y1 = m(x2 − x1)
The equation of the line is therefore
The midpoint of the line joining two points
Once we know the coordinates of two points on a straight line, we can find the mid-point of the line.
Distance between two points
The distance formula is derived from the Pythagoras theorem. To find the distance between two points, if A is (x1 , y1) and B is (x2 , y2), all that you need to do is use the coordinates of these ordered pairs.
The distance between two points is given by:
In our next class, we will be talking more about the Coordinate Geometry of straight line. We hope you enjoyed the class.
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