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UNIT 08 March
1. Find the coordinates of the vector with the followings initial and terminal points:
𝒂𝒂) 𝑰𝑰𝑷𝑷 = (𝟏𝟏, 𝟒𝟒); 𝑻𝑻𝑷𝑷 = (𝟑𝟑, −𝟐𝟐)
𝒃𝒃) 𝑰𝑰𝑷𝑷 = (𝟗𝟗, −𝟏𝟏); 𝑻𝑻𝑷𝑷 = (𝟓𝟓, −𝟐𝟐)
𝒄𝒄) 𝑰𝑰𝑷𝑷 = (−𝟏𝟏, −𝟒𝟒); 𝑻𝑻𝑷𝑷 = (−𝟑𝟑, −𝟐𝟐)
𝒅𝒅) 𝑰𝑰𝑷𝑷 = (𝟏𝟏𝟎𝟎, 𝟏𝟏𝟒𝟒); 𝑻𝑻𝑷𝑷 = (𝟏𝟏, −𝟏𝟏)
𝒆𝒆) 𝑰𝑰𝑷𝑷 = (−𝟐𝟐, 𝟑𝟑); 𝑻𝑻𝑷𝑷 = (−𝟏𝟏, 𝟑𝟑)
2. Find the magnitude of the vectors formed by these points:
𝒂𝒂) 𝑰𝑰𝑷𝑷 = (𝟏𝟏, 𝟒𝟒); 𝑻𝑻𝑷𝑷 = (𝟑𝟑, −𝟐𝟐)
𝒃𝒃) 𝑰𝑰𝑷𝑷 = (𝟗𝟗, −𝟏𝟏); 𝑻𝑻𝑷𝑷 = (𝟓𝟓, −𝟐𝟐)
𝒄𝒄) 𝑰𝑰𝑷𝑷 = (−𝟏𝟏, −𝟒𝟒); 𝑻𝑻𝑷𝑷 = (−𝟑𝟑, −𝟐𝟐)
𝒅𝒅) 𝑰𝑰𝑷𝑷 = (𝟏𝟏𝟎𝟎, 𝟏𝟏𝟒𝟒); 𝑻𝑻𝑷𝑷 = (𝟏𝟏, −𝟏𝟏)
𝒆𝒆) 𝑰𝑰𝑷𝑷 = (−𝟐𝟐, 𝟑𝟑); 𝑻𝑻𝑷𝑷 = (−𝟏𝟏, 𝟑𝟑)
3. Are these vectors parallel or perpendicular?
𝒂𝒂) 𝒖𝒖��⃗ = (𝟏𝟏, 𝟑𝟑); 𝒗𝒗��⃗ = (−𝟏𝟏, −𝟑𝟑)
𝒃𝒃) 𝒖𝒖��⃗ = (𝟑𝟑, 𝟐𝟐); 𝒗𝒗��⃗ = (−𝟔𝟔, −𝟒𝟒)
𝒄𝒄) 𝒖𝒖��⃗ = (𝟐𝟐, 𝟒𝟒); 𝒗𝒗��⃗ = (𝟐𝟐, −𝟏𝟏)
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.1.1
UNIT 08 March
4. Draw the triangle of vertices (𝟏𝟏, 𝟏𝟏); (𝟑𝟑, 𝟑𝟑) and (𝟔𝟔, 𝟎𝟎) and find the coordinates of
the vectors 𝑨𝑨𝑨𝑨������⃗; 𝑩𝑩𝑩𝑩������⃗ and 𝑪𝑪𝑪𝑪�����⃗.
5. Find all Initial point of the vector 𝒖𝒖��⃗ = (𝟑𝟑, −𝟏𝟏) knowing that the terminal point is
𝑻𝑻𝑻𝑻(𝟓𝟓, 𝟐𝟐).
6. The vertices of a rhombus are 𝑨𝑨(𝟏𝟏, 𝟒𝟒); 𝑩𝑩(𝟎𝟎, 𝟐𝟐); 𝑪𝑪(𝟏𝟏, 𝟎𝟎) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑫𝑫(𝟐𝟐, 𝟐𝟐). Find the
length of the diagonals and its area.
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.1.2

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4 ESO Academics - Unit 08 - Exercises 4.8.1 - Vectors.

  • 1. UNIT 08 March 1. Find the coordinates of the vector with the followings initial and terminal points: 𝒂𝒂) 𝑰𝑰𝑷𝑷 = (𝟏𝟏, 𝟒𝟒); 𝑻𝑻𝑷𝑷 = (𝟑𝟑, −𝟐𝟐) 𝒃𝒃) 𝑰𝑰𝑷𝑷 = (𝟗𝟗, −𝟏𝟏); 𝑻𝑻𝑷𝑷 = (𝟓𝟓, −𝟐𝟐) 𝒄𝒄) 𝑰𝑰𝑷𝑷 = (−𝟏𝟏, −𝟒𝟒); 𝑻𝑻𝑷𝑷 = (−𝟑𝟑, −𝟐𝟐) 𝒅𝒅) 𝑰𝑰𝑷𝑷 = (𝟏𝟏𝟎𝟎, 𝟏𝟏𝟒𝟒); 𝑻𝑻𝑷𝑷 = (𝟏𝟏, −𝟏𝟏) 𝒆𝒆) 𝑰𝑰𝑷𝑷 = (−𝟐𝟐, 𝟑𝟑); 𝑻𝑻𝑷𝑷 = (−𝟏𝟏, 𝟑𝟑) 2. Find the magnitude of the vectors formed by these points: 𝒂𝒂) 𝑰𝑰𝑷𝑷 = (𝟏𝟏, 𝟒𝟒); 𝑻𝑻𝑷𝑷 = (𝟑𝟑, −𝟐𝟐) 𝒃𝒃) 𝑰𝑰𝑷𝑷 = (𝟗𝟗, −𝟏𝟏); 𝑻𝑻𝑷𝑷 = (𝟓𝟓, −𝟐𝟐) 𝒄𝒄) 𝑰𝑰𝑷𝑷 = (−𝟏𝟏, −𝟒𝟒); 𝑻𝑻𝑷𝑷 = (−𝟑𝟑, −𝟐𝟐) 𝒅𝒅) 𝑰𝑰𝑷𝑷 = (𝟏𝟏𝟎𝟎, 𝟏𝟏𝟒𝟒); 𝑻𝑻𝑷𝑷 = (𝟏𝟏, −𝟏𝟏) 𝒆𝒆) 𝑰𝑰𝑷𝑷 = (−𝟐𝟐, 𝟑𝟑); 𝑻𝑻𝑷𝑷 = (−𝟏𝟏, 𝟑𝟑) 3. Are these vectors parallel or perpendicular? 𝒂𝒂) 𝒖𝒖��⃗ = (𝟏𝟏, 𝟑𝟑); 𝒗𝒗��⃗ = (−𝟏𝟏, −𝟑𝟑) 𝒃𝒃) 𝒖𝒖��⃗ = (𝟑𝟑, 𝟐𝟐); 𝒗𝒗��⃗ = (−𝟔𝟔, −𝟒𝟒) 𝒄𝒄) 𝒖𝒖��⃗ = (𝟐𝟐, 𝟒𝟒); 𝒗𝒗��⃗ = (𝟐𝟐, −𝟏𝟏) Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.1.1
  • 2. UNIT 08 March 4. Draw the triangle of vertices (𝟏𝟏, 𝟏𝟏); (𝟑𝟑, 𝟑𝟑) and (𝟔𝟔, 𝟎𝟎) and find the coordinates of the vectors 𝑨𝑨𝑨𝑨������⃗; 𝑩𝑩𝑩𝑩������⃗ and 𝑪𝑪𝑪𝑪�����⃗. 5. Find all Initial point of the vector 𝒖𝒖��⃗ = (𝟑𝟑, −𝟏𝟏) knowing that the terminal point is 𝑻𝑻𝑻𝑻(𝟓𝟓, 𝟐𝟐). 6. The vertices of a rhombus are 𝑨𝑨(𝟏𝟏, 𝟒𝟒); 𝑩𝑩(𝟎𝟎, 𝟐𝟐); 𝑪𝑪(𝟏𝟏, 𝟎𝟎) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑫𝑫(𝟐𝟐, 𝟐𝟐). Find the length of the diagonals and its area. Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.1.2