Mathematics • Year 8 • Unit 2 • Lesson 2
Plotting — Mixed Challenge
Pull together everything from Lesson 2: reading, plotting, comparing positions, and working with decimal coordinates. Six mixed problems, one "find the mistake", and one open-ended challenge about points that line up on a horizontal or vertical line.
1. Mixed problems — choose the right move
Each question uses a different idea from Lesson 2. Decide BEFORE you write what's being asked. Show your reasoning. 3 marks each
1.1 Describe how to plot the point (−6, 3) starting from the origin. Use "left/right" and "up/down".
1.2 A point P is plotted 4 units to the right and 7 units below the origin. Write its coordinates and state its quadrant.
1.3 Describe how to plot the decimal point (−1.5, 2.5). Use "halfway between" in your description.
1.4 Three points (4, 1), (4, −2) and (4, 5) all share the same x-value. (a) Are they on a horizontal or vertical line? (b) Write down one other point on the same line.
1.5 Three points (−2, 5), (0, 5) and (3, 5) all share the same y-value. (a) Are they on a horizontal or vertical line? (b) Write the coordinates of the point on this line that also lies on the y-axis.
1.6 Two friends each describe a point. Anna says "go 3 left, 4 down". Ben says "the point (−3, 4)". (a) Plot or describe both as coordinate pairs. (b) Are they the same point? Why or why not?
2. Find the mistake
Another student tried to plot the point M(−2, 5). Their written instructions are below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's instructions — plot M(−2, 5):
Line 1: Start at the origin (0, 0).
Line 2: x = −2, so move 2 units to the right.
Line 3: y = 5, so from there move 5 units up.
Line 4: Mark and label the point M. It is in Quadrant II.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong, and what the result of the mistake would be (where the dot would actually end up).
(c) Write out the corrected instructions in full, ending with the correct quadrant.
Stuck? Check the sign of x = −2. A negative x means LEFT, not right.3. Open-ended challenge — points on the same line
This question has more than one valid answer. 4 marks
3.1 Find three different points (with different x and y values) that ALL lie on the same horizontal line as (−1, 3). Then find three different points that ALL lie on the same vertical line as (−1, 3).
For each set, write a one-sentence rule that describes every point on the line.
Bonus: for the vertical line, include at least one point with a NEGATIVE y-value.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Plot (−6, 3)
Start at the origin. Move 6 units left along the x-axis, then 3 units up. Mark a dot. Point lies in Quadrant II.
1.2 — Point P
4 right → x = 4; 7 below → y = −7. So P(4, −7), pattern (+, −) → Quadrant IV.
1.3 — Plot (−1.5, 2.5)
Start at the origin. Move 1.5 units to the left — halfway between the −1 and −2 gridlines on the x-axis. Then move 2.5 units up — halfway between the 2 and 3 gridlines on the y-axis. Mark the dot midway between grid intersections, in Quadrant II.
1.4 — Points sharing x = 4
(a) They lie on a vertical line (the line x = 4).
(b) Any other point with x = 4 works, e.g. (4, 0), (4, 10), or (4, −7).
1.5 — Points sharing y = 5
(a) They lie on a horizontal line (the line y = 5).
(b) The point on y = 5 that also has x = 0 is (0, 5) — it sits on the y-axis.
1.6 — Anna vs Ben
(a) Anna: "3 left, 4 down" → x = −3, y = −4 → (−3, −4). Ben: (−3, 4).
(b) No, they are different points. Anna's point has y = −4 (below the x-axis, Quadrant III); Ben's has y = +4 (above the x-axis, Quadrant II). They share the same x but have opposite y signs — they are mirror images across the x-axis.
2 — Find the mistake
(a) The mistake is on Line 2.
(b) x = −2 is NEGATIVE, so we should move 2 units LEFT, not right. With the student's mistake the dot would end up at (2, 5) instead of (−2, 5) — a completely different point in Quadrant I.
(c) Corrected instructions:
Line 1: Start at the origin (0, 0).
Line 2: x = −2, so move 2 units to the LEFT.
Line 3: y = 5, so from there move 5 units up.
Line 4: Mark and label M. It is in Quadrant II. ✓
3 — Points on the same line (sample solution)
Same horizontal line as (−1, 3) — y must equal 3: e.g. (0, 3), (4, 3), (−5, 3). Rule: every point on this line has y = 3.
Same vertical line as (−1, 3) — x must equal −1: e.g. (−1, 0), (−1, 7), (−1, −4). Rule: every point on this line has x = −1.
Bonus: the vertical-line set above includes (−1, −4), which has a negative y-value. ✓
Marking: 1 mark per valid set of three distinct points (2 marks total). 1 mark for each correct one-sentence rule (2 marks total). Bonus point folded into the mark for the vertical set.