Chapter 7: Geometry, Coordinates, and Transformations
Geometry, Coordinates and Transformations
Use precise geometric facts and coordinate rules to describe shapes, angles and movement clearly.
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Step-by-step teaching, practice and checkpoint.
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Workbook pages
Fun Maths Book 3 pages 77-88
Use angle facts, polygons, circles, coordinates, translations, 3D shapes and nets.
Think first
Good mathematicians decide what the question is asking before they calculate.
- 1Which geometry fact applies here?
- 2Are we reading an angle, a coordinate, a movement or a solid shape?
- 3For coordinates, have we moved across first and then up or down?
- 4Can we check the answer against the diagram or shape?
Visual teaching
See the method
Angle arms rotate on a straight line, a point moves by a column vector and a 3D net folds into a solid.
Worked examples
Two angles on a straight line are 127 degrees and x. Find x.
Step 1: What information is given?
One angle is 127 degrees, and the other angle is x.
Why: We need to match the question to an angle fact.
Step 2: Which angle fact should we use?
Angles on a straight line add to 180 degrees.
Why: A straight line makes a half turn.
Be careful: Do not use 360 degrees; that is for angles around a point.
Step 3: Now calculate the missing angle.
180 - 127 = 53.
Why: The two angles together must total 180 degrees.
Common mistake: Using 360 degrees for a straight-line angle question.
Translate (4, 5) by the vector (3, -2).
Step 1: What does the first coordinate tell us?
The point starts at x = 4 and y = 5.
Why: Coordinates are read across first, then up.
Step 2: What does the vector mean?
(3, -2) means move 3 right and 2 down.
Why: The first vector number changes x, and the second changes y.
Be careful: Do not add both numbers to the same coordinate.
Step 3: Apply the movement.
x: 4 + 3 = 7. y: 5 - 2 = 3.
Why: Each coordinate changes by its matching vector part.
Common mistake: Reversing x and y, or treating -2 as +2.
A triangle has angles 48 degrees, 67 degrees and y. Find y.
Step 1: What geometric fact applies?
Angles in a triangle add to 180 degrees.
Why: This fact lets us find a missing triangle angle.
Step 2: What do the known angles total?
48 + 67 = 115.
Why: Add the known parts before finding the missing part.
Step 3: Now find the missing angle.
180 - 115 = 65.
Why: The three angles must total 180 degrees.
Common mistake: Subtracting each angle from 180 separately.
Guided practice
Translate (2, 7) by the vector (4, -3).
Independent practice
Your turn
Angles around a point add to...
Translate (2, 7) by (4, -3).
Which solid has two circular faces?
Mini checkpoint
Check your thinking
Angles around a point add to...
A triangle has angles 35 degrees and 78 degrees. What is the third angle?
Which solid has two circular faces?
Key idea
Geometry depends on matching the question to the correct fact, then checking the diagram or movement. Use angle totals, read coordinates across then up, describe translations precisely, and check shapes using their properties.
Parent signal
Watch whether coordinates are reversed. Across first, then up is the key habit.