If the point (x, y) be equidistant from the points (a + b, b - a) and (a - b, a + b), prove that
a-b/a+b = x-y/x+y
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(3, 7), (6, 5) and (15, –1)
=>Let the points be A (15, –1), B (6, 5) and C (3, 7)
Distance of AB
⇒ AB = √ (6 – 15)2 + (5 – (–1))2
⇒ AB = √ (–9)2 + (6)2
⇒ AB = √ (81 + 36)
⇒ AB = √ 117 = √ 3 × 3 × 13
⇒ AB = 3√13
Distance of BC
⇒ BC = √ (3 – 6)2 + (7 – 5)2
⇒ BC= √ (3)2 + (2)2
⇒ BC = √ (9 + 4)
⇒ BC= √ 13
Distance of AC
⇒ AC = √ (3 – 15)2 + (7 – (–1))2
⇒ AC = √ (3 – 15)2 + (7 + 1)2
⇒ AC= √ (–12)2 + (8)2
⇒ AC = √ (144 + 64)
⇒ AC= √ 208 = √ 4 × 4 × 13
⇒ AC = 4√13
i.e. AB + BC = AC
⇒ 3√13 + √13 = 4√13
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