P is one-third and Q is two-thirds along the segment. The total change in x is 12 and y is –9. Applying these shifts to A gives P (8, 4) and Q (12, 1).
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Use the midpoint formula: x-mid = (x1 + x2) / 2. For x: –7 = (3 + x) / 2 which gives x = –17. For y: 1 = (–4 + y) / 2 which gives y = 6. Point ...
Check the change in y over the change in x. From R to B: (–5 – –1) / (–2 – –5) = –4/3. From B to C: (–12 – –5) / (4 – –2) = –7/6. Slopes differ, so they ...
(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.
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.