AI generatedGeometry and measuresGCSE Higher / IGCSE Extended

Finding one unknown for collinear points

Finding one unknown for collinear points.

  • Find two vectors sharing one point, such as AB and AC.
  • Show one is a single scalar multiple of the other, using the same scalar for every component.
  • State both facts: parallel vectors and a common point. Therefore the three points are collinear.

Example 1

A = (1, 2), B = (3, 5) and C = (, 8). Find so that A, B and C are collinear.

Subtract A from B component by component.Subtract A from C.
ScalarUse the known -components to find the common scalar.
Use that same scalar for the -components.Add 1 to both sides.

Example 2

A = (2, 3), B = (5, 7) and C = (, 15). Find so that A, B and C are collinear.

Subtract A from B component by component.Subtract A from C.
ScalarUse the known -components to find the common scalar.
Use that same scalar for the -components.Add 2 to both sides.

Your turn

Question 1

A = (3, 4), B = (7, 9) and C = (, 24). Find so that A, B and C are collinear.

Check answer
Subtract A from B component by component.Subtract A from C.
ScalarUse the known -components to find the common scalar.
Use that same scalar for the -components.Add 3 to both sides.
Question 2

A = (4, 2), B = (6, 8) and C = (, 32). Find so that A, B and C are collinear.

Check answer
Subtract A from B component by component.Subtract A from C.
ScalarUse the known -components to find the common scalar.
Use that same scalar for the -components.Add 4 to both sides.
Question 3

A = (1, 3), B = (4, 6) and C = (, 21). Find so that A, B and C are collinear.

Check answer
Subtract A from B component by component.Subtract A from C.
ScalarUse the known -components to find the common scalar.
Use that same scalar for the -components.Add 1 to both sides.
Question 4

A = (2, 4), B = (6, 8) and C = (, 12). Find so that A, B and C are collinear.

Check answer
Subtract A from B component by component.Subtract A from C.
ScalarUse the known -components to find the common scalar.
Use that same scalar for the -components.Add 2 to both sides.
Question 5

A = (3, 2), B = (5, 7) and C = (, 17). Find so that A, B and C are collinear.

Check answer
Subtract A from B component by component.Subtract A from C.
ScalarUse the known -components to find the common scalar.
Use that same scalar for the -components.Add 3 to both sides.
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