Worksheet: Parallel Vectors and Collinear Points

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

Q1:

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

Q2:

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.

Q3:

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

  • AYes
  • BNo

Q4:

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

  • ANo
  • BYes

Q5:

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

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