Question

Line AB contains points A (0, 0) and B (2, 2). Line CD contains points C (3, 1) and D (5, 3). Lines AB and CD are

A. parallel
B.perpendicular
C.neither

Answer 1

It is parallel because if you graph the points on graph paper they come out parallel.

Answer 2

Option A is correct.

Lines AB and CD are parallel.

Explanation:

Parallel lines: They have the same slope and will never intersects.

Perpendicular lines : The slope of the perpendicular are negative reciprocal to each other.

As per the statement:

Line AB contains points A (0, 0) and B (2, 2).

Slope the two points is given by:

`\text{Slope} = (y_2-y_1)/(x_2-x_1)`

then;

`\text{Slope AB} = (2-0)/(2-0)=(2)/(2)=1`

Similarly for:

Line CD contains points C (3, 1) and D (5, 3)

then;

`\text{Slope CD} = (3-1)/(5-3)=(2)/(2)=1`

Since, the slope of AB = Slope of CD

then by definition:

⇒Lines AB and CD are parallel.