1. Find the length of the hypotenuse in the following right-angled triangle

2. Recall
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3. Determine the distance between the two points (2,5) and (5,9)

4. Distance between 2 points
(Length of a straight line segment)

5. Determine the distance between the two points (2,5) and (5,9)x
4 units
(2,5)
3 units

6. Distance between 2 points
Using the distance formula

7. Determine the distance between the two points (2,5) and (5,9)
(x1 , y1)
(x2 , y2)
(5,9)
x2 – x1 d
y2 – y1
4 units
(2,5)
d2 = (x2 – x1)2 + (y2 – y1)2
3 units

8. Formula
Distance between two points A(x1 , y1) and B(x2 , y2) is given by:
│AB│= √ (x2 – x1)2 + (y2 – y1)2
Note: Distance between two points is also referred to the length of a straight line segment.

9. Homework Task
In ∆ABC, where A(3, 4) , B(-5, 10) and C(-13, 4), determine the length of: AB AC BC
What type of triangle does ∆ABC represents.

10. Recap:
State the steps involved in determining the distance between 2 points:
By completing a right-angled triangle
Using the Distance Formula

11. Final Evaluation
Determine the distance between the points A(-3, -1) and B(7, 4) using the distance formula.