Line QR contains (2, 8) and (3, 10) Line ST contains points (0, 6) and (- 2,2). Are lines QR and ST parallel or perpendicular?

Solution:

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

Line QR comprises points (2,8) and (3,10).

From these two points the slope of the line m₁ can be calculated as

m₁ = (y₂ - y₁) / (x₂ - x₁)

= (10 - 8) / (3 - 2)

= 2

Line ST comprises points (0,6) and (-2,2).

From these two points the slope of the line m₁ can be calculated as

m₂ = (y₂ - y₁) / (x₂ - x₁)

= (2 - 6) / (-2 - 0)

= -4 / -2

= 2

Since the slopes of Lines QR and ST are the same it can be concluded that the two lines are parallel.

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Line QR contains (2, 8) and (3, 10) Line ST contains points (0, 6) and (- 2,2). Are lines QR and ST parallel or perpendicular?

Summary:

The slope of the two lines is the same and hence the lines are parallel.