(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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Yes, they are collinear. One method is comparing the ratio of coordinates (y/x). For M, –4 divided by –3 equals 4/3; for G, 8 divided by 6 equals 4/3. Since ratios match, they are on one line.
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.
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).
The general observations remain the same, but the specific changes swap. The x-coordinates would stay the same, while the y-coordinates would change their signs. The triangle would flip vertically instead of horizontally.