This document discusses plane coordinate geometry and includes four activities involving using coordinates to determine distances and locations on a coordinate plane. The activities have students: 1) Find distances between points on a number line using coordinates and relate segment lengths. 2) Determine missing side lengths of right triangles using coordinates. 3) Find distances between houses, a plaza, city hall, and a gas station using their coordinates on a plane. 4) Plot points on a plane, find their intersections, and determine distances and coordinates using formulas.

1. PLANE COORDINATE
GEOMETRY

2. INTRODUCTION
•Look around! What geometric figures do
you see in your classroom, school
buildings, houses, bridges, roads, and
other structures?
•Have you ever asked yourself how
geometric figures helped in planning the
construction of these structures?

3. •In your community or province, was
there any instance when a stranger or a
tourist asked you about the location of
place or landmark?
•Were you able to give the right direction
and how far it is?

4. THE DISTANCE FORMULA, MIDPOINT
FORMULA AND THE COORDINATE PROOF
• Activity 1: How Long Is This Part?
• Use the number line below to find the length of each of the following
segments and then answer the questions that follow.

5. •1.) AB
•2.) BC
•3.) CD

6. •4.) DE
•5.) EF
•6.) FG

7. • How did you find the length of each segment?
• Did you use the coordinates of the points in finding the length of each
segment?
• If yes, how?

8. • 4.) How would you relate the lengths of the following segments?
• 1.) AB, BC, and AC
• 2.) AC, CE, and AE

9. • 5.) Is the length of AD the same as the length of DA? How about BF
and FB? Explain your answer.

10. Activity 2: I am Right
• The length of one side of each right triangle is unknown. Determine
the length of this side. Explain how you obtained your answer.

11. Activity 3: Let’s Exercise!
• Jose lives 5 km away from the plaza. Every Saturday, he meets Emilio
and Diego for a morning exercise. In going to the plaza, Emilio has to
travel 6km to the west, while Diego has to travel 8km to the south.
The location of their houses and the plaza are illustrated on the
coordinate plane as shown.

12. • How far is Emilio’s house from Diego’s house? Explain your answer.
• Suppose the City Hall is 4km north of Jose’s house. How far is it from
the plaza? From Emilio’s house? Explain your answer.
• How far is the gasoline station from Jose’s house if it is 4km south of
Emilio’s house? Explain your answer.

13. • What are the coordinates of the points corresponding to the houses
of Jose, Emilio, and Diego? How about the coordinates of the point
corresponding to the plaza?

14. • If the City hall is 4km north of Jose’s house, what are the coordinates
of the point corresponding to it? How about the coordinates of the
point corresponding to the gasoline station if it is 4km south of
Emilio’s house?

15. • How are you going to use the coordinates of the points in
determining the distance between Emilio’s house and the City Hall?
Jose’s house and the gasoline station? The distance of the houses of
Jose, Emilio, and Diego from each other? Explain your answer.

16. • Did you learn something new about this activity?
• What did you learned?

17. Activity 4: Let Me Formulate!
• 1.) Plot the points A(2,1) and B(8,9) on the coordinate plane.
• 2.) Draw a horizontal line passing through A and a vertical line
containing B.

18. • 3.) Mark and label the point of intersection of the two lines as C.
• What are the coordinates of C? Explain how you obtained your
answer.
• What is the distance between A and C?
• How about the distance between B and C?

19. • 4.) Connect A and B by a line segment.
• What kind of triangle is formed by A, B, and C? Explain your answer.
• How will you find the distance between A and B?
• What is AB equal to?

20. • 5.) Replace the coordinates of A by (x1,y1) and B(x2,y2)
• What would be the resulting coordinates of C?
• What expression represents the distance between A and C?
• How about the expression that represents the distance between B
and C?
• What equation will you use to find the distance between A and B?
Explain your answer.