Vertex — Grade 7 Accelerated, what it means and where it is taught
A flat surface; a line where two faces meet; a corner point.
Taught in Grade 7 Accelerated.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Face — A flat surface; a line where two faces meet; a corner point.
What uses it later
This idea is needed for:
- Central angle — An angle whose vertex is the centre. Equal to its arc.
- Inscribed angle — An angle whose vertex is on the circle. Half its arc.
Practise this idea
18 questions in the course bank use Vertex, in Length and Area in 2-D Figures, Geometric Construction, Problem Solving, Translations, Reflections & Rotations, Angle Relationships, Absolute Value, Piecewise & Step Functions. The first 8 are below; the rest are in those units.
Problem 1
A triangle has its base along the full 12-unit side of a 12 × 8 rectangle, with its third vertex on the opposite side. Find its area.
Worked answer
48
Base = 12, height = 8
12(12)(8) = 48
Exactly half the rectangle — and it does not matter where along the side the apex sits.
Problem 2
A triangle has interior angles of 60° and 70°. Find the exterior angle at the third vertex.
Worked answer
130
Third interior angle: 180 - 60 - 70 = 50°
Exterior angle: 180 - 50 = 130°
Or directly: 60 + 70 = 130° ✓
Problem 3
How many diagonals does a hexagon have?
Worked answer
9
Each vertex connects to 6 - 3 = 3 others by a diagonal
6 × 3 = 18, counting each diagonal twice
18 ÷ 2 = 9
Problem 4
Triangle ABC has A(1, 2), B(5, 2), C(1, 6). Its image is A'(2, -1), B'(2, -5), C'(6, -1). Which transformation was used?
Worked answer
rotation of 90 degrees clockwise about the origin
A(1,2) → (2, -1) ✓
B(5,2) → (2, -5) ✓
C(1,6) → (6, -1) ✓
That rule is a 90° clockwise rotation, also called 270° counter-clockwise
Problem 5
A triangle has interior angles 38° and 59°. Find the exterior angle at the third vertex.
Worked answer
97
38 + 59 = 97
97°
Problem 6
An isosceles triangle has a vertex angle of 44°. Find each base angle.
Worked answer
68
180 - 44 = 136
136 ÷ 2 = 68
68°
Problem 7
Find the vertex of y = |x - 5|.
Worked answer
(5, 0)
x - 5 = 0 when x = 5
y = 0 there
Problem 8
The graph of y = -|x| + 2 has a vertex at (0, 2) and
- opens downward
- opens upward
- is a straight line
- is a parabola
Worked answer
opens downward
-|x| turns the V upside down
So (0, 2) is a maximum