Analytical Geometry Distance formula lesson

1. ANALYTIC GEOMETRY
LESSON 2

2. DISTANCE
FORMULA
MS. NIEZEL MAE L. TIPLES

3. 𝑷𝟏 𝒙𝟏, 𝒚𝟏
𝑷𝟐 𝒙𝟐, 𝒚𝟐
Q 𝒙𝟐, 𝒚𝟏
Pythagorean Theorem
𝒄𝟐 = 𝒂𝟐 + 𝒃𝟐

4. Distance Formula
The distance, 𝑑 units, between two points with
coordinates 𝑥1, 𝑦1 and 𝑥2, 𝑦2 is given by the following
formula.
𝒅 = 𝒙𝟐 − 𝒙𝟏
𝟐 + 𝒚𝟐 − 𝒚𝟏
𝟐

5. EXAMPLE 1
Find the length of the line segment.
Solution:
1, 3 , −2, −2
𝑑 = 𝑥2 − 𝑥1
2 + 𝑦2 − 𝑦1
2

6. EXAMPLE 2
Find the length of the line segment.
Solution:
1, 1 , −1, −1
𝑑 = 𝑥2 − 𝑥1
2 + 𝑦2 − 𝑦1
2

7. EXAMPLE 3
If 𝑃1 = 𝑥, 0 , 𝑃2 2, 5 , and 𝑃1𝑃2 = 5 2, find 𝑥.
Solution:
𝑑 = 𝑥2 − 𝑥1
2 + 𝑦2 − 𝑦1
2

8. EXAMPLE 4
Determine whether A = 1, 7 , 𝐵 0, 3 , and
𝐶 −2, −5 are collinear.
Solution:

9. EXAMPLE 5
Show that 1, 2 , 4, 7 , −6, 13 and −9, 8
are the vertices of a rectangle.
Solution:

10. EXAMPLE 6
Prove analytically that the diagonals of a
rectangle are equal.

11. “Mathematics is not about
numbers, equations,
computations, or algorithms; it is
about UNDERSTANDING”.
- WILLIAM PAUL THURSTON