4 ESO Academics - Unit 08 - Exercises 4.8.2 - Operations with Vectors. Relationship between Points in the Plane.

1. UNIT 08 March
1. Draw and solve. Data: 𝑨𝑨(𝟎𝟎, 𝟎𝟎); 𝑩𝑩(−𝟏𝟏, 𝟑𝟑); 𝑪𝑪(−𝟐𝟐, −𝟐𝟐); 𝑫𝑫(𝟏𝟏, −𝟑𝟑)
𝒂𝒂) 𝑨𝑨𝑨𝑨������⃗ + 𝑪𝑪𝑪𝑪������⃗
𝒃𝒃) 𝑪𝑪𝑪𝑪������⃗ − 𝑨𝑨𝑨𝑨������⃗
𝒄𝒄) 𝑪𝑪𝑪𝑪������⃗ − 𝑪𝑪𝑪𝑪������⃗
𝒅𝒅) 𝑨𝑨𝑨𝑨������⃗ − 𝑪𝑪𝑪𝑪������⃗
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.2.1

2. UNIT 08 March
𝒆𝒆) 𝑨𝑨𝑨𝑨������⃗ + 𝑨𝑨𝑨𝑨������⃗
𝒇𝒇) 𝑩𝑩𝑩𝑩������⃗ + 𝑫𝑫𝑫𝑫������⃗
2. Solve:
𝒂𝒂) 𝟑𝟑 ∙ (𝟏𝟏, 𝟐𝟐)
𝒃𝒃) 𝟐𝟐 ∙ (−𝟐𝟐, 𝟓𝟓) − 𝟑𝟑 ∙ (−𝟓𝟓, −𝟐𝟐)
𝒄𝒄) − 𝟓𝟓 ∙ (𝟏𝟏, 𝟏𝟏) + 𝟑𝟑 ∙ (−𝟐𝟐, −𝟐𝟐) − 𝟒𝟒(−𝟏𝟏, 𝟏𝟏)
3. Find the coordinates of the midpoints of the sides of this quadrilateral?
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.2.2

3. UNIT 08 March
4. The segments 𝑨𝑨𝑨𝑨 and 𝑩𝑩𝑩𝑩 have the same midpoint. If (−𝟐𝟐, 𝟑𝟑) , 𝑩𝑩(−𝟑𝟑, −𝟏𝟏) and
𝑪𝑪(𝟒𝟒, −𝟐𝟐) , find the coordinates of the point 𝑫𝑫.
5. Find, in each case, the symmetric of 𝑨𝑨(−𝟑𝟑, − 𝟓𝟓) with respect to:
𝒂𝒂) 𝑷𝑷(−𝟐𝟐, 𝟎𝟎)
𝒃𝒃) 𝑸𝑸(𝟐𝟐, − 𝟑𝟑)
𝒄𝒄) 𝑶𝑶(𝟎𝟎, 𝟎𝟎)
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.2.3

4. UNIT 08 March
6. Find the value of “𝒂𝒂” in order that the points 𝑷𝑷(𝟐𝟐, 𝟕𝟕), 𝑸𝑸(𝟓𝟓, −𝟏𝟏) and 𝑹𝑹(𝒂𝒂, −𝟐𝟐𝟐𝟐)
are on the same straight line.
7. Find the distance between 𝑷𝑷 and 𝑸𝑸.
𝒂𝒂) 𝑷𝑷(−𝟖𝟖, 𝟑𝟑) , 𝑸𝑸(−𝟔𝟔, 𝟏𝟏)
𝒃𝒃) 𝑷𝑷(−𝟑𝟑, 𝟎𝟎) , 𝑸𝑸(𝟏𝟏𝟏𝟏, 𝟎𝟎)
8. Prove that the triangle with vertices (𝟒𝟒, 𝟒𝟒) , 𝑩𝑩(−𝟐𝟐, 𝟑𝟑) and 𝑪𝑪(𝟑𝟑, −𝟐𝟐) is isosceles.
What are the two equal sides? Find the area of this triangle.
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.2.4