(i) Right-angled isosceles: O (0, 0), A (5, 0), B (0, 5). (ii) Isosceles: O (0, 0), P (–3, –4) in Quadrant III and Q (3, –4) in Quadrant IV. Both triangles have two equal side lengths.
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Without negative numbers, the system would only include Quadrant I, where both coordinates are positive. This restricted system would not allow us to locate points in the other three quadrants of a full 2-D plane.
Plot Z at (5, –6) in Quadrant IV. If we choose I(5, 0) and N(0, 0), side IZ = 6 units, IN = 5 units and by the Baudhāyana-Pythagoras Theorem, ZN = √61 units.
(i) Sides AM and MP are perpendicular. (ii) Side AM is parallel to the x-axis. (iii) Points M(–5, –2) and P (–5, 2) are mirror images across the x-axis. Plotting verifies these geometric relationships.
A line through W parallel to the y-axis keeps the x-coordinate constant at –5. Thus, H will have coordinates (–5, y). H can lie in Quadrant II (if y > 0) or Quadrant III (if y < 0).