,
Coordinate Geometry : more straight lines
 

[ parallel ][ perpendicular][ equation y = mx + c ]

[intersection point][ equ. 1 point+gradient ][ equ. 2 points ]

 

 

 

 

Parallel lines

parallel lines

Parallel lines make equal corresponding angles(θ) with the x-axis. Therefore their gradients are equal.

 

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Perpendicular lines

two lines perependicular to each other

If two lines are perpendicular to eachother, the product of their gradients is -1.

If the gradient of AB is m1 and the gradient of CD is m2 , then:

gradients of 2 perpendicular lines

 

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Equation of a straight line y = mx + c

equation of a straight line

The equation of a straight line is given by:

y=mx +c  equation of a straight line

Example

What is the equation of the straight line with gradient 3 that crosses the y-axis at y= -3 ?

equation of a straight line problem#1

 

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Finding the intersection point between two straight lines

There are two types of problem here. One where the lines are not perpendicular to eachother and the other when they are.

To solve the former all that is needed is to solve the equations of the lines simultaneously.

With the later, only one equation is given and the second equation must be worked out from the information supplied. then it is a matter of proceding as before ie to solve the two equations simultaneously.

Example #1

Find the intersection point of the two straight lines:

intersection problem#1

Example #2

A straight line y = 2x + 4.5 intersects another perpendicularly. If the second straight line has an intercept of -0.5 on the y-axis, what are the coodinates of the point of intersection of the two lines? (answer to 1 d.p.)

intersection problem#2

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Finding the eq. of a straight line from one point + gradient

Solution is by using the expression for gradient(m) for an actual point(x1,y1) and a generalized point(x,y).

gradient of a straight line

The straight line equation is found by substituting values of x1, y1 and m into the above.

Example

A line of gradient 3 passes through a point (2,5). What is the equation of the line?

y=mx + c problem#1

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Finding the equation of a straight line from two points

Solution is by first finding the gradient m from the x and y values from the points (x1,y1) and (x2,y2)

gradient#3

Then we use the expression again, but this time with one actual point and a generalized point(x,y).

gradient of a straight line

The straight line equation is found by substituting for x1, y1 and m.

Example

Find the equation of the line between the two points (2,3) and (-5,7).

equation of a straight line from 2 points problem#2

 

 

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