Using vertex properties: A = E + F – D, giving (1, 7). B = D + F – E, giving (–1, –1). C = D + E – F, giving (11, 3). These coordinates form the original triangle ABC.
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Radius squared is 1 squared plus –8 squared, which is 65. For D: (–5) squared plus 6 squared is 61. Since 61 is less than 65, D is inside. For E: 0 squared plus 9 squared is 81. E is ...
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).
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 ...