Mathematics • Year 8 • Unit 2 • Lesson 1
The Cartesian Plane
Build fluency with the axes, the origin, ordered pairs and the four quadrants. One worked example, one guided example with blanks, then eight independent problems from naming quadrants to working with points on the axes.
1. I do — fully worked example
Read every line. Each step explains why, not just what, so you can copy the same thinking later.
Problem. Which quadrant contains the point P(−3, 5)?
Step 1 — Read the coordinates in order: x first, y second.
x = −3, y = 5
Reason: every ordered pair is written (x, y). The first number is always horizontal, the second always vertical.
Step 2 — Read the signs.
x is negative (−), y is positive (+) → sign pattern (−, +)
Reason: the SIGN of each coordinate decides the side of each axis — left/right for x, up/down for y.
Step 3 — Match the sign pattern to a quadrant.
I = (+,+) II = (−,+) III = (−,−) IV = (+,−)
Reason: quadrants are numbered anticlockwise starting from the top right. (−, +) lands in the top-left region.
Answer: P(−3, 5) is in Quadrant II.
2. We do — fill in the missing steps
Same shape as Section 1, but the working has gaps. Fill every blank in pencil. 4 marks
Problem. Which quadrant contains the point Q(2, −7)?
Step 1 — Read coordinates in order: x = ______, y = ______.
Step 2 — Read the signs:
x is ______ (sign), y is ______ (sign) → pattern ( __ , __ )
Step 3 — Match the pattern to a quadrant:
Pattern ( __ , __ ) = Quadrant ______
Step 4 — Final answer:
Q(2, −7) is in Quadrant ______.
3. You do — independent practice
Show your reasoning in the space under each problem. Problems 3.1–3.4 are foundation (single-quadrant identify). 3.5 and 3.6 are standard (points on axes, multi-step). 3.7 and 3.8 are extension (reasoning about a missing coordinate).
Foundation — name the quadrant
3.1 Which quadrant contains A(4, 7)? 1 mark
3.2 Which quadrant contains B(−2, −6)? 1 mark
3.3 Which quadrant contains C(5, −3)? 1 mark
3.4 Which quadrant contains D(−9, 1)? 1 mark
Standard — points on axes / multi-step
3.5 A point E has coordinates (0, −4). It is not in any quadrant. Explain in one sentence WHY, then state which axis it lies on. 2 marks
3.6 A point F is 6 units to the LEFT of the origin and 2 units UP. Write the coordinates of F and state its quadrant. 2 marks
Extension — reason about a missing coordinate
3.7 A point G(p, −5) lies in Quadrant III. What can you say about the sign of p? Give one possible whole-number value of p. 2 marks
3.8 Points H(3, 0) and J(0, 3) look similar but are NOT in the same place. Describe — in one sentence each — where each one sits on the plane. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do Q(2, −7)
Step 1: x = 2, y = −7.
Step 2: x is positive, y is negative → pattern (+, −).
Step 3: (+, −) = Quadrant IV.
Step 4: Q(2, −7) is in Quadrant IV.
3.1 — A(4, 7)
Both positive → (+, +) → Quadrant I.
3.2 — B(−2, −6)
Both negative → (−, −) → Quadrant III.
3.3 — C(5, −3)
x positive, y negative → (+, −) → Quadrant IV.
3.4 — D(−9, 1)
x negative, y positive → (−, +) → Quadrant II.
3.5 — E(0, −4)
Because x = 0 the point has not moved left or right from the origin, so it lies on an axis. With y = −4 it sits 4 units BELOW the origin, on the y-axis. Points on an axis are not counted in any quadrant.
3.6 — F is 6 left, 2 up
6 units left → x = −6. 2 units up → y = 2. So F(−6, 2), pattern (−, +) → Quadrant II.
3.7 — G(p, −5) in Quadrant III
Quadrant III requires both coordinates negative, so p must be negative (p < 0). Any negative whole number works, e.g. p = −1 (or −2, −3, …). The point would then be G(−1, −5).
3.8 — H(3, 0) vs J(0, 3)
H(3, 0): y = 0, so H sits on the x-axis, 3 units to the right of the origin.
J(0, 3): x = 0, so J sits on the y-axis, 3 units above the origin.
Same numbers, different order → completely different addresses. Order matters in (x, y).