Yes, it is a square. All four sides (AB, BC, CD, DA) equal the square root of 10. Both diagonals (AC and BD) equal the square root of 20. The total area is 10.
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(i) No part is outside. For A: 100 minus 80 is 20 (within 0 to 800). For B: 250 plus 100 is 350 (within 0 to 800). (ii) Distance between centers is 170. Sum of radii is 180. They intersect.
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.
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).