4 ESO Academics - Unit 08 - Exercises 4.8.3. - Lines.

1. UNIT 08 March
1. Find the vector equation of a line that pass through the points:
𝒂𝒂) 𝑨𝑨(𝟒𝟒, 𝟒𝟒) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟐𝟐, 𝟑𝟑)
𝒃𝒃) 𝑨𝑨(−𝟏𝟏, 𝟑𝟑) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟏𝟏, 𝟓𝟓)
2. Find the parametric equations of a line that pass through the points:
𝒂𝒂) 𝑨𝑨(𝟒𝟒, 𝟒𝟒) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟐𝟐, 𝟑𝟑)
𝒃𝒃) 𝑨𝑨(−𝟏𝟏, 𝟑𝟑) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟏𝟏, 𝟓𝟓)
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.3.1

2. UNIT 08 March
3. Find the vector equation of a line with direction vector parallel to the line
(𝒙𝒙, 𝒚𝒚) = (𝟎𝟎, 𝟐𝟐) + 𝐭𝐭 ∙ (𝟑𝟑, 𝟏𝟏) and pass through the point (−𝟏𝟏, 𝟓𝟓).
4. Find the parametric equations of parallel line to a line with direction vector
𝒗𝒗��⃗ = (𝟑𝟑, 𝟓𝟓) and pass through the point (𝟎𝟎, 𝟐𝟐).
5. Find the symmetric equations of a line that pass through the points:
𝒂𝒂) 𝑨𝑨(𝟒𝟒, 𝟒𝟒) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟐𝟐, 𝟑𝟑)
𝒃𝒃) 𝑨𝑨(−𝟏𝟏, 𝟑𝟑) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟏𝟏, 𝟓𝟓)
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.3.2

3. UNIT 08 March
6. Find the point-slope form of a equations of a line that pass through the points:
𝒂𝒂) 𝑨𝑨(𝟒𝟒, 𝟒𝟒) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟐𝟐, 𝟑𝟑)
𝒃𝒃) 𝑨𝑨(−𝟏𝟏, 𝟑𝟑) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟏𝟏, 𝟓𝟓)
7. Find the point-slope form of a equations of a line that pass through origin point
and its direction vector is 𝒗𝒗��⃗ = (𝟑𝟑, 𝟐𝟐).
8. Find the point-slope form of a equations of a line that pass through the point
𝑨𝑨(𝟏𝟏, 𝟏𝟏) and is parallel to 𝒚𝒚 = −𝟐𝟐𝟐𝟐
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.3.3

4. UNIT 08 March
9. Find the slope-intercept form of a equations of a line that pass through the
points:
𝒂𝒂) 𝑨𝑨(𝟒𝟒, 𝟒𝟒) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟐𝟐, 𝟑𝟑)
𝒃𝒃) 𝑨𝑨(−𝟏𝟏, 𝟑𝟑) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟏𝟏, 𝟓𝟓)
10. Find the general equation of a line that pass through the points:
𝒂𝒂) 𝑨𝑨(𝟒𝟒, 𝟒𝟒) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟐𝟐, 𝟑𝟑)
𝒃𝒃) 𝑨𝑨(−𝟏𝟏, 𝟑𝟑) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟏𝟏, 𝟓𝟓)
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.3.4

5. UNIT 08 March
11. Given the line 𝒙𝒙 − 𝟒𝟒𝟒𝟒 + 𝟓𝟓 = 𝟎𝟎, find:
a) Its direction vector.
b) One point of the line.
c) A perpendicular vector.
12. Find all the equations of a line that pass through the points:
𝒂𝒂) 𝑨𝑨(𝟎𝟎, 𝟎𝟎) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(−𝟒𝟒, 𝟑𝟑)
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.3.5

6. UNIT 08 March
𝒃𝒃) 𝑨𝑨(−𝟐𝟐, −𝟑𝟑) 𝒂𝒂𝒏𝒏𝒏𝒏 𝑩𝑩(𝟏𝟏, −𝟓𝟓)
13. Find all the relative position of the lines:
𝒂𝒂)
𝒚𝒚 = −𝟐𝟐𝟐𝟐 + 𝟏𝟏
𝟐𝟐𝟐𝟐 − 𝟑𝟑 + 𝟐𝟐 = 𝟎𝟎
�
𝒃𝒃)
(𝒙𝒙, 𝒚𝒚) = (𝟐𝟐, 𝟑𝟑) + 𝒕𝒕 ∙ (𝟏𝟏, 𝟒𝟒)
𝒙𝒙 − 𝟑𝟑
−𝟖𝟖
=
𝒚𝒚 − 𝟏𝟏
−𝟐𝟐
�
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.3.6

7. UNIT 08 March
14. Find a perpendicular line and a parallel line to the line 𝟒𝟒𝒙𝒙 + 𝟑𝟑𝟑𝟑 + 𝟐𝟐 = 𝟎𝟎 that
pass through the point 𝑷𝑷(𝟑𝟑, −𝟏𝟏).
15. Find the vector equation of a perpendicular line to the line 𝒂𝒂𝒙𝒙 + 𝒚𝒚 − 𝟓𝟓 = 𝟎𝟎 that
pass through the point 𝑷𝑷(𝟎𝟎, 𝟒𝟒). Draw it.
16. Given the equation 𝒚𝒚 =
𝟑𝟑
𝟐𝟐
𝒙𝒙 + 𝟏𝟏.
a) Find a parallel line that pass through the point 𝑨𝑨(𝟎𝟎, 𝟐𝟐).
b) Find the point-slope form of a perpendicular line that pass through the origin.
c) Find the symmetric equation of a parallel line that pass through point 𝑩𝑩(𝟏𝟏, 𝟐𝟐).
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.8.3.7