This document explains the distance formula and how to use it to calculate the distance between points on a Cartesian plane. It provides the steps to use the Pythagorean theorem to derive the distance formula: take the difference between the x-coordinates squared and add it to the difference between the y-coordinates squared, and take the square root of the result. It then works through an example of using the distance formula to calculate the distance between points (3,2) and (8,7), which equals 5 units. The document concludes with practice problems and assignments applying the distance formula.

1. DISTANCE FORMULA

2. Plot these coordinates on
our Cartesian plane.
(3,2)
(8,7)
(8,2)

8. RIGHT TRIANGLE

9. AC is
plotted on
the x- axis.

10. Find the difference of the two
coordinates in x axis.
x2-x1
x2=8
x1=3
=8 – 3
=5

11. AC is
plotted on
the x- axis.
BC is plotted on the y-axis

12. Find the difference of the two
coordinates in x axis.
y2-y1
y2=7
y1=2
=7 – 2
=5

13. PYTHAGOREAN
THEOREM

14. 푐 = 푥2 − 푥1
2 + (푦2 − 푦1)2

15. DISTANCE FORMULA

16. SUBSTITUTION METHOD
By substitution:
퐷 = 푥2 − 푥1
2 + (푦2 − 푦1)2
퐷 = 5 2 + 5 2
퐷 = 50

17. ACTIVITY #1
• Graph and show that the following
coordinates forms an isosceles
triangle by using the distance
formula.
S (-1,4)
C (0,1)
B (2,5)

22. 퐵푆 = 푥2 − 푥1
2 + (푦2 − 푦1)2
= 2 + 1 2 + (5 −4)2
= 10

23. QUIZ#6
Get ½ crosswise sheet of pad paper and
answer the following.
Find the distance between the given
points.
1. (0,9) and (0,13)
2. (4,5) and (-3,5)
3. (8,1) and (8,-2)
4. (1,0) and (5,2)
5. (5,-4) and (1,-1)

24. ASSIGNMENT
A. Graph and Find the distance using
distance formula.
I (-4,6)
V (2,5)
Y (-1,6)
S (5, 10)
B. Make a research on midpoint and
give at least 2 examples.