Chapter G4 Section 7

Parallel and Perpendicular

Line Criteria using slope

Perpendicular Lines:

Lines are perpendicular if and only if their

slopes are opposite reciprocals

Ex 2: l1 = -2. Find l2 so that l1 ⊥ l2.

Parallel Lines:

Lines are parallel if and only if their

slopes are the same.

Ex 2: l1 = -3. Find l2 so that l1 || l2.

Ex 1: 𝑚1 =3

5. Find 𝑚2 so that 𝑚1||𝑚2.

𝑚2 = 3

5

𝑚2 = −3

Reminder: Lines can have Zero slopes and

Undefined slopes.

y = equation

x = equation VERTICAL LINE!!!

HORIZONTAL LINE!!!

0

#= 𝑧𝑒𝑟𝑜 𝑠𝑙𝑜𝑝𝑒

#

0= 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑠𝑙𝑜𝑝𝑒

Zero slope and undefined slopes are ⊥ lines!

Ex 1: l1 contains the points (-3, 3) and (5, 2).

l2 contains the points (-1, -4) and (0, 1).

Are l1 and l2 parallel, perpendicular, or neither?

NEITHER

Ex 2: Line a contains the points (-2, 2) and (5, 8).

Line b contains the points (1, 6) and (-6, 0).

Are a and b parallel, perpendicular, or neither?

||

𝑏 =0 − 6

−6 − 1 =

−6

−7 =

6

7

𝑎 =8 − 2

5 + 2 =

6

7

neither

Ex 3: Are the segments through the origin and

the points listed parallel, perpendicular or

neither?

𝐴 −7, −9 , 𝐵(−9, −7)

𝑠𝑙𝑜𝑝𝑒 𝐴 𝑡𝑜 𝑜𝑟𝑖𝑔𝑖𝑛 = −9 − 0

−7 − 0 =

−9

−7 =

9

7

𝑠𝑙𝑜𝑝𝑒 𝐵 𝑡𝑜 𝑜𝑟𝑖𝑔𝑖𝑛 = −7 − 0

−9 − 0 =

−7

−9 =

7

9

⊥

Ex 4: Given 𝑋(1, 4) and 𝑌(−3, 6) and 𝑍 listed

below, are segments 𝑋𝑌 and 𝑌𝑍 parallel,

perpendicular, or neither.

𝑍(−4, 4)

𝑠𝑙𝑜𝑝𝑒 𝑋𝑌 =6 − 4

−3 − 1 =

1

−2

𝑠𝑙𝑜𝑝𝑒 𝑌𝑍 = 6 − 4

−3 + 4 =

2

1 = 2

= 2

−4

𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝐴𝐶 =

Ex 5: Given A(0, 0) and B(-4, 5), find the

coordinates of a point C in quadrant I so that

𝐴𝐶 ⊥ 𝐴𝐵.

𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝐴𝐵 = 5 − 0

−4 − 0 =

5

−4

4

5

4

5=

𝑦 − 0

𝑥 − 0

4

5=

𝑦

𝑥

(5, 4)