AI generatedGeometry and measuresGCSE Higher

Vectors to a midpoint

Express the midpoint in terms of the given vectors.

  • A vector has both magnitude and direction. Reverse a route by changing its sign.
  • Use a consistent direction and match corresponding components.
  • A scalar multiple proves parallel directions. Collinearity also needs a shared point.

Example 1

M is the midpoint of .

Find the whole directed vector from A to B.Use 1 of the 2 total ratio parts.Add the route O → A → M.

Find the position vector of M. The denominator uses the total number of parts.

Example 2

M is the midpoint of .

Find the whole directed vector from A to B.Use 1 of the 2 total ratio parts.Add the route O → A → M.

Find the position vector of M. The denominator uses the total number of parts.

Your turn

Question 1

M is the midpoint of .

Check answer
Find the whole directed vector from A to B.Use 1 of the 2 total ratio parts.Add the route O → A → M.
Question 2

M is the midpoint of .

Check answer
Find the whole directed vector from A to B.Use 1 of the 2 total ratio parts.Add the route O → A → M.
Question 3

M is the midpoint of .

Check answer
Find the whole directed vector from A to B.Use 1 of the 2 total ratio parts.Add the route O → A → M.
Question 4

M is the midpoint of .

Check answer
Find the whole directed vector from A to B.Use 1 of the 2 total ratio parts.Add the route O → A → M.
Question 5

M is the midpoint of .

Check answer
Find the whole directed vector from A to B.Use 1 of the 2 total ratio parts.Add the route O → A → M.
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