Worksheet: Parallel Vectors and Collinear Points

In this worksheet, we will practice proving whether vectors are parallel and whether points are collinear.


If the points (0,3), (4,6), and (8,𝑎) are collinear, find the value of 𝑎.


Consider the points 𝐴(1,2), 𝐵(5,7), 𝐶(1,8), and 𝐷(1,𝑎). If 𝐴𝐵 is parallel to 𝐶𝐷, find the value of 𝑎.


Consider the points 𝐴(1,2), 𝐵(3,5), 𝐶(3,6), and 𝐷(7,12). Is 𝐴𝐵 parallel to 𝐶𝐷?

  • AYes
  • BNo


Are the points (1,2), (3,4), and (11,8) collinear?

  • ANo
  • BYes


Consider the points 𝐴(1,2), 𝐵(7,5), 𝐶(6,9), and 𝐷(10,3).

Find 𝐴𝐵.

  • A8,3
  • B7,2
  • C8,3
  • D7,10
  • E5,7

Find 𝐶𝐷.

  • A16,6
  • B4,12
  • C60,27
  • D16,6
  • E10,9

Is 𝐴𝐵 parallel to 𝐶𝐷?

  • ANo
  • BYes

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.