Everything Maths Grade 10

Parallel and perpendicular lines EMA6D

Two lines that run parallel to each other are always the same distance apart and have equal gradients.

If two lines intersect perpendicularly, then the product of their gradients is equal to1.

If lineW X?Y Z, thenmW XmY Z= 1. Perpendicular lines have gradients that are the negative inverses
of each other.
VISIT:
The following video shows some examples of calculating the slope of a line and determining if two lines are
perpendicular or parallel.
See video:2GCJatwww.everythingmaths.co.za

Worked example 6: Parallel lines

QUESTION

Prove that lineABwithA(0; 2)andB(2; 6)is parallel to lineCDwith equation 2 xy= 2.

SOLUTION

Step 1: Draw a sketch

 4  2 2 4

 4

 2

2

4

6

A(0;2)

B(2;6)

y=2x 2

x

y

(Be careful - some lines may look parallel but are not!)

Step 2: Write down the formula for gradient

m=

y 2 y 1

x 2 x 1

Step 3: Substitute values to find the gradient for lineAB

mAB=

6 2

2 0

=

4

2

= 2

300 8.3. Gradient of a line