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in Two Dimensional Analytical Geometry by (46.9k points)
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The point on the line 2x – 3y = 5 is equidistance from (1, 2) and (3, 4) is … 

(a) (7, 3) 

(b) (4, 1) 

(c) (1, -1) 

(d) (-2, 3)

1 Answer

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Best answer

(b) (4, 1)

Let (a, b) be on 2x – 3y = 5 ⇒ 2a – 3b = 5 

It is equidistance from (1, 2) and (3, 4)

(a – 1)2 + (b – 2)2 = (a – 3)2 + (6 – 4)2 

a2 – 2a + 1 + b2 – 4b + 4 = a2 – 6a + 9 + b2 – 8b + 16

4a + 4b = 20 

2a + 2b = 10 

2a – 3b = 5 

5b = 5 

b = 1 

∴ a = 4 

∴ The point is (4, 1)

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