parallel & perpendicular lines

PARALL

EL &

PERPE

NDICULA

R

LINES

10

MA

TH

@ S

CS

C

PARALLEL LINES

Parallel lines are lines that: Never intersect Have the same slope Hence the same gradient

m1= m2

You already know that the equation of a linear graph can be written in the form of

where m is the gradient and b is the y-coordinate of the y-intercept (0,b)

You should be able to manipulate the equation to show that the gradient is the same and hence the lines are parallel.

See chapter 4.4, worked example 11

PARALLEL LINES: ACTIVITY

Find a real life example of parallel lines (not from the internet) and annotate the image to prove the lines are parallel

Remember, parallel lines are lines that: Never intersect Have the same slope Hence the same gradient

On your image annotate to show the following: Cartesian plane Rise and run The equation of both lines Find the gradient of each equation and prove that the lines are

parallel

PERPENDICULAR LINES

Lines that are perpendicular intersect at right angles (90°).

We can show this when we rotate our coordinate points 90° clockwise/anticlockwise.

Example

The line has the x-intercept pf (2,0) and the y-intercept of (0,4). If these points are rotated 90° anticlockwise about the origin they will be positioned at (0,2) and (-4,0). Joining these points will give us s line perpendicular to

We know that when lines are perpendicular, the product of their gradient is -1.

m1m2=-1

In the above example m1=-2 and m2= When we multiply m1 by m2 we obtain -1

m1m2= -2 x

m1m2= -1

PERPENDICULAR LINES: ACTIVITY

Find a real life example of perpendicular lines (not from the internet) and annotate the image to prove the lines are parallel

Remember, perpendicular lines are lines that intersect at right angles (90°).

On your image annotate to show the following: Cartesian plane Find the equation of both lines Identify the gradients m1 and m2 of each equation and multiply to

determine whether m1 x m2 = -1

CHAPTER 4.4 QUESTIONS

ENTRY

Q1a, Q2a, Q3 a e i, Q4 a e i, Q5, Q7-9, Q17

EXPECTED

Q1, Q2, Q3 a e i, Q4 a e i, Q5, Q7-9, Q15, Q17

EXPECTED +

Q1, Q2, Q3 a e i, Q4 a e i, Q5, Q7-9, Q11, Q15, Q17