Mathematics • Year 8 • Unit 2 • Lesson 2
Plotting Points and Coordinates
Build fluency in two directions: reading the coordinates of a plotted point, and plotting a point from its coordinates. One worked example, one guided example with blanks, then eight independent problems including decimal coordinates.
1. I do — fully worked example
Two skills are happening at once: reading a point AND plotting a point. We'll walk through both directions.
Problem. Plot the point P(−3, 2) on a Cartesian plane, then describe how you did it.
Step 1 — Start at the origin (0, 0).
Reason: every (x, y) coordinate is measured FROM the origin. The origin is your launch pad.
Step 2 — Move x first: x = −3 means 3 units LEFT.
Origin (0, 0) → land at (−3, 0) on the x-axis.
Reason: the first coordinate is always horizontal. Negative means left; positive means right.
Step 3 — Then move y: y = 2 means 2 units UP.
From (−3, 0) → up to (−3, 2). Mark a clear dot. Label it "P(−3, 2)".
Reason: the second coordinate is always vertical. Positive means up; negative means down.
Step 4 — Check the quadrant matches the signs.
x = −3 (negative), y = 2 (positive) → pattern (−, +) → Quadrant II.
Reason: a quick sanity check. Left + up = top-left = Quadrant II. ✓
Answer: P sits 3 left and 2 up from the origin, in Quadrant II.
2. We do — fill in the missing steps
Same shape as Section 1, but now you fill the gaps. 4 marks
Problem. Plot the point Q(4, −1) and describe how.
Step 1 — Start at the ______.
Step 2 — Move x first: x = 4 means ______ units to the ______.
After Step 2 we are at (______ , 0) on the ______-axis.
Step 3 — Then move y: y = −1 means ______ unit ______.
After Step 3 we are at the point ( ____ , ____ ).
Step 4 — Sign pattern check: ( ____ , ____ ) → Quadrant ______.
3. You do — independent practice
Show your reasoning. 3.1–3.4 are foundation (read or plot a single integer point). 3.5–3.6 are standard (decimal coordinates from the lesson). 3.7–3.8 are extension (reasoning about points that line up).
Foundation — read or plot a point
3.1 Describe how to plot A(5, 2) starting from the origin. Use the words "right" and "up". 1 mark
3.2 Describe how to plot B(−4, −2). Use "left" and "down". 1 mark
3.3 A point C is plotted 6 units right of the origin and 3 units down. Write its coordinates. 1 mark
3.4 A point D is plotted 2 units left of the origin and 7 units up. Write its coordinates and state its quadrant. 1 mark
Standard — decimal coordinates
3.5 Describe how to plot E(2.5, −1.5). Use "right/left", "up/down" and the word "halfway". 2 marks
3.6 A point F sits exactly halfway between (3, 4) and (3, 6) on a vertical grid line. Write F's coordinates. 2 marks
Extension — reasoning about points that line up
3.7 Three points G(2, 1), H(2, 4) and J(2, −3) all share something. (a) What do they share? (b) What kind of line do they sit on? 2 marks
3.8 Without plotting, decide which point is closer to the origin: K(3, 4) or L(5, 0). Briefly explain your reasoning. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do Q(4, −1)
Step 1: start at the origin.
Step 2: x = 4 means 4 units to the right. After Step 2 we are at (4, 0) on the x-axis.
Step 3: y = −1 means 1 unit down. After Step 3 we are at (4, −1).
Step 4: (+, −) → Quadrant IV.
3.1 — Plot A(5, 2)
Start at the origin, move 5 units right, then 2 units up. Mark a dot and label it A.
3.2 — Plot B(−4, −2)
Start at the origin, move 4 units left, then 2 units down. Mark a dot and label it B.
3.3 — Point C
6 right → x = 6. 3 down → y = −3. So C(6, −3).
3.4 — Point D
2 left → x = −2. 7 up → y = 7. So D(−2, 7), pattern (−, +) → Quadrant II.
3.5 — Plot E(2.5, −1.5)
Start at the origin. Move 2.5 units right — that's halfway between the 2 and 3 grid lines on the x-axis. Then move 1.5 units down — halfway between the −1 and −2 grid lines on the y-axis. Mark a dot midway between grid intersections. E lies in Quadrant IV.
3.6 — F halfway between (3, 4) and (3, 6)
Both points share x = 3, so they sit on a vertical grid line. The halfway y is (4 + 6) ÷ 2 = 5. So F(3, 5).
3.7 — G(2, 1), H(2, 4), J(2, −3)
(a) All three points share the same x-value of 2.
(b) They all lie on the vertical line x = 2 (a vertical line through x = 2 on the x-axis).
3.8 — Closer to the origin: K(3, 4) or L(5, 0)?
L(5, 0) is on the x-axis, exactly 5 units from the origin. K(3, 4) forms a right triangle with legs 3 (across) and 4 (up); the hypotenuse from origin to K is √(3² + 4²) = √25 = 5 units. So K and L are exactly the same distance from the origin — both are 5 units away.