Chapter 7: Coordinate, Ratio and Proportion

Fans Cherry's, Jun 3, 2025

Chapter 7: Coordinate, Ratio and Proportion

Table of Contents

  1. Coordinate
    1. Coordinates
    2. Quiz for Coordinates
  2. Ratio
    1. Note and Example
    2. Quiz Ratio
    3. Exercise Ratio
  3. Proportion
    1. Notes and Example
    2. Exercise Proportion
    3. PROPORTION QUIZ
  4. Augmented Reality
    1. Plotting Points in 3D: AR Template
    2. AR Ratio
    3. AR for Coordinates Question 1

1.

Coordinate

  • 1. Coordinates
  • 2. Quiz for Coordinates

1.1.

Coordinates

What is coordinates?
Coordinates are a pair of numbers that show the exact position of a point on a map or graph.[br][list][*] The [color=#0000ff][b]origin[/b][/color] is the starting point, which is (0,0).[/*][*]The distance along the [color=#0000ff][b]y-axis[/b][/color] is the vertical distance.[/*][*]The distance along the [color=#0000ff][b]x-axis[/b][/color] is the horizontal distance.[/*][/list]
Horizontal and Vertical Distance from the Origin (pg 235)
[list=1][size=100][*]The horizontal distance of the parrot from the ticket counter is [color=#0000ff][b]4 units[/b][/color].[/*][*]The vertical distance from the ticket counter to the jetty is [color=#0000ff][b]5 units[/b][/color].[/*][*]The horizontal distance from the origin to the lion is [color=#0000ff][b]5 units[/b][/color], and the vertical distance is [color=#0000ff][b]3 units[/b][/color].[/*][/size][/list]
Horizontal and Vertical Distances Between Two Coordinates (page 236)
[size=100]Answer:[br]2 units horizontally (to the right)[br]5 units vertically (upwards)[/size]
– winkee, Fans Cherry's

1.2.

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2.

Ratio

  • 1. Note and Example
  • 2. Quiz Ratio
  • 3. Exercise Ratio

2.1.

Note and Example

What is Ratio?
[list][*]Ratio is the comparison of the size or value of one quantity with another.[/*][*]It involves comparing two quantities of the same kind. [/*][*]These quantities can be the number of objects, measurements of length, weight, or volume. [/*][*]Ratios can be simplified.[/*][/list]
How to write ratio?
[b]Example: [/b][b]If there are 3 apples and 5 oranges[/b][br][list][*]The ratio of [color=#0000ff]apples to oranges [/color]is [color=#0000ff]3 : 5.[br][/color][/*][*]The fractional form is[color=#0000ff] [/color][math]\frac{3}{5}[/math][color=#0000ff].[/color][/*][*][color=#980000][b]Order [/b][/color]is important!!! Ratio of apples : oranges [math]\ne[/math] ratio of oranges : apples. [/*][*][color=#980000][b]Unit of measurement [/b][/color]must be [color=#980000][b]same [/b][/color]for both quantities. [/*][/list]
Picture1
Example 1A
The table shows the length of fabric purchased by Raysha's mother.[br][table][tr][td][b]Fabric color[/b][/td][td]Yellow[/td][td]Green[/td][td]Blue[/td][/tr][tr][td][b]Length[/b][/td][td]2m[/td][td]300cm[/td][td]4m[/td][/tr][/table][br]State the ratio: [br]a) Length of yellow fabric to the length of green fabric.[br][br][color=#134f5c][b]Answer: [/b] [br]Yellow = 2m [br]Green = 300cm = 3m [br][/color][color=#ff0000][b]*The unit of measurement must be the same.[/b][/color][color=#134f5c][br][br]Yellow : Geen[br] 2 : 3[br][/color]
Example 1B
The table shows the length of fabric purchased by Raysha's mother.[br][table][tr][td][b]Fabric color[/b][/td][td]Yellow[/td][td]Green[/td][td]Blue[/td][/tr][tr][td][b]Length[/b][/td][td]2m[/td][td]300cm[/td][td]4m[br][/td][/tr][/table][br]State the ratio: [br]b) Length of blue fabric to the total length of all fabric.[br][br][color=#134f5c][b]Answer: [/b] [br]Green = 300cm = 3m[br][/color][b][color=#ff0000]*The unit of measurement must be the same.[br][/color][/b][color=#134f5c] [br]Blue = 4m [br]Total fabric = Yellow + Blue + Green[br]      =2+3+4[br]    =9[br]Blue : Total fabric[br] 4 : 9[/color]
Example 1C
The table shows the length of fabric purchased by Raysha's mother.[br][table][tr][td][b]Fabric color[/b][/td][td]Yellow[/td][td]Green[/td][td]Blue[/td][/tr][tr][td][b]Length[/b][/td][td]2m[/td][td]300cm[/td][td]4m[br][/td][/tr][/table][br]State the ratio: [br]c) Total length of all fabric to the length of yellow fabric.[br][br][color=#134f5c][b]Answer: [/b] [br]Green = 300cm = 3m[br][/color][b][color=#ff0000]*The unit of measurement must be the same.[/color][/b][color=#134f5c][br]Yellow=2m[br]Total fabric = Yellow + Blue + Green[br]    =2+3+4[br]    =9[br]All fabric : Yellow[br] 9 : 2[/color]
Picture 2
Example 2a
Based on Picture 2, the mass of each watermelon is the same. State the ratio:[br]a) the mass of one watermelon to the mass of one pineapple[br][br][color=#134f5c][b]Answer: [br][/b]2 watermelon = 4kg[br]1 watermelon = [/color][math]\frac{4}{2}[/math][color=#134f5c]kg[br] = 2 kg[br][br]1watermelon + 1 pineapple = 3kg[br]  2kg + 1 pineapple = 3kg[br] 1 pineapple = 3kg-2kg[br]  = 1kg[br][/color][br][color=#1155cc]*1 watermelon = 2kg[br]*1 pineapple = 1kg[br][br][/color][color=#134f5c]1 watermelon : 1 pineapple[br] 2 : 1[/color]
Example 2b
Based on Picture 2, the mass of each watermelon is the same. State the ratio:[br]b) the mass of one pineapple to the total mass of the fruits[br][br][b]Answer:[br][/b][color=#0000ff]*1 watermelon = 2kg[br]*1 pineapple = 1kg[/color][br][color=#134f5c][br]Total mass of fruits = 3 watermelon + 1 pineapple[br][/color]          [color=#134f5c] = 3 x 2kg + 1kg[br]         = 6kg + 1kg[br]          = 7kg[br][/color][br][color=#134f5c]Total fruits : 1 pineapple[br][/color][color=#134f5c] 7 : 1[/color]
Example 3
The price of one pair of pants is 3 times the price of one shirt. State the ratio of the price of one shirt to the total price of one shirt and one pair of pants.[br][br][color=#134f5c][b]Answer:[br][/b]1 pants = 3 shirt[br]Change to fractional form : [/color][math]\frac{pants}{shirt}[/math][color=#134f5c]=[/color][math]\frac{3}{1}[/math][color=#134f5c][br]Change to ratio: [br][/color][color=#1155cc]* pants : shirt[br] 3 : 1[br][br][/color][color=#134f5c]Total 1 pants + 1 shirt= 3 + 1[br][/color]       [color=#134f5c]  = 4[/color][br][color=#134f5c]1 Shirt : Total[br][/color][color=#134f5c] 1 : 4[/color]
– Fans Cherry's

2.2.

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2.3.

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3.

Proportion

  • 1. Notes and Example
  • 2. Exercise Proportion
  • 3. PROPORTION QUIZ

3.1.

Notes and Example

[size=150][b][u][size=200]PROPORTION[/size][/u][/b][/size]
What is proportion?
[list][*]Comparing two quantities or numbers [/*][*]Showing equality between two ratios[/*][/list]How to read:[br][color=#0000ff]4kg[/color] of biscuits costing [color=#ff7700]RM58[/color] is proportional to [color=#ff0000]2kg[/color] of biscuits costing[color=#00ff00]RM29[/color][br] [color=#0000ff]4kg[/color]:[color=#ff7700]RM58[/color] [color=#ff0000] 2kg[/color]:[color=#00ff00]RM29[/color]
Contoh 1
[size=100][b]Calculate the mass of butter for 2 batches of batik cake[br][br]Step 1:[br]Write the ratio of the mass of butter for 2 cups of cooking chocolate[br][br]1 cup of cooking chocolate 200 g butter[br][br]2 cups of cooking chocolate ? g butter[br][br]Step 2:[br]Calculate the mass of butter[br][br]200 g [math]\times[/math]2= 400 g[br][br]Answer:[br]The mass of butter for 2 batches of the recipe is[color=#0000ff] 400 g[/color][/b][/size]
Contoh 2
[size=150][b]Calculate the price for 2 kg 400g green beans[/b][/size][br]2kg 400g=2kg +400g[br][br][justify][b][size=100]Step 1:[br]Write the ratio for price and mass in the scale.[/size][/b][/justify][table][tr][td]1kg[math]:RM8.5[/math][/td][td][br][/td][/tr][tr][td]2kg[math]:2\times RM8.5=RM17[/math][/td][td][br][/td][/tr][/table][br][table][tr][td]1000g[math]:RM8.5[/math][/td][td][/td][/tr][tr][td]100g[math]:RM0.85[/math][/td][td][/td][/tr][/table][table][tr][td]400g[math]:4\times RM0.85=RM3.40[/math][/td][td][br][/td][/tr][/table][justify][/justify][size=100][b]Step 2 :[/b][/size][table][tr][td][b][/b][/td][td][br][/td][/tr][tr][td]RM17+RM3.4=RM20.40[/td][td][br][/td][/tr][/table][br][justify][b][/b][/justify][size=100][justify][b]Answer:[br]Price for 2kg 400g green beans is [color=#0000ff]RM 20.40[/color][/b][/justify][/size]
– LIEW JB, Yrou Cheong, Arthur Lee

3.2.

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3.3.

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4.

Augmented Reality

  • 1. Plotting Points in 3D: AR Template
  • 2. AR Ratio
  • 3. AR for Coordinates Question 1

4.1.

Plotting Points in 3D: AR Template

Directions:
1) Open up GeoGebra 3D app on your device. Press AR button to activate Augmented Reality. [br][br]2) Go to MENU. Select SEARCH. [br] Type [b]gagsx5fv[/b] access this resource right away. (Note how this ID can be found in this URL). [br][br]3) Note the sliders that exist in the algebra view. [br] [b][color=#9900ff]a = x coordinate[/color][br][/b] [b] [color=#38761d]b = y-coordinate[/color][br] [color=#ff7700]c = z-coordinate[/color][/b][br][br]4) Move the slider [b]plotpoint[/b] to plot the point (a, b, c). [br]
– Tim Brzezinski

4.2.

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4.3.

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Information