FIND WHETHER THE LINE JOINING TWO POINTS ARE PARALLEL OR PERPENDICULAR

Determine whether AB is parallel to CD.

Problem 1 :

A(5, 6), B(-1, 3), C(-4, 9), D(-16, 3)

Solution:

Slope of AB:

A(5, 6) ==>(x₁, y₁), B(-1, 3) ==> (x₂, y₂)

Slope of CD:

C(-4, 9) ==>(x₁, y₁), D(-16, 3) ==> (x₂, y₂)

Slope of AB = Slope of CD

1/2 = 1/2

So, slope of the lines AB and CD are equal.

Hence, the line AB is parallel to CD.

Problem 2 :

A(-3, 6), B(5, 4), C(-14, -10), D(-2, -7)

Solution:

Slope of AB:

A(-3, 6) ==>(x₁, y₁), B(5, 4) ==> (x₂, y₂)

Slope of CD:

C(-14, -10) ==>(x₁, y₁), D(-2, -7) ==> (x₂, y₂)

Slope of AB ≠ Slope of CD

-1/4 ≠ 1/4

So, the lines are neither parallel nor perpendicular.

Problem 3 :

A(6, -3), B(5, 2), C(-4, -4), D(-5, 2)

Solution:

Slope of AB:

A(6, -3) ==>(x₁, y₁), B(5, 2) ==> (x₂, y₂)

Slope of CD:

C(-4, -4) ==>(x₁, y₁), D(-5, 2) ==> (x₂, y₂)

Slope of AB ≠ Slope of CD

-5 ≠ -6

So, the lines are neither parallel nor perpendicular.

Problem 4 :

A(-5, 6), B(-7, 2), C(7, 1), D(4, -5)

Solution:

Slope of AB:

A(-5, 6) ==>(x₁, y₁), B(-7, 2) ==> (x₂, y₂)

Slope of CD:

C(7, 1) ==>(x₁, y₁), D(4, -5) ==> (x₂, y₂)

Slope of AB = Slope of CD

2 = 2

So, slope of the lines AB and CD are equal.

Hence, the line AB is parallel to CD.