Question

If the mid point of the line segment joining the points A (x + y, x - y) and B (3x - y, - x - y) is (2, 1) then length of AB is​

Answer 1

Solution :-

since (2,1) is mid point of the line segment joining the points A (x + y, x - y) and B (3x - y, - x - y) ,

→ 2 = (x + y + 3x - y)/2

→ 4 = 4x

→ x = 1

and,

→ 1 = (x - y - x - y)/2

→ 2 = -2y

→ y = (-1)

then,

→ coordinates of A = (x + y, x - y) = (1 - 1 , 1 + 1) = (0, 2)

→ coordinates of B = (3x - y, - x - y) = (3*1 + 1, -1 + 1) = (4, 0)

therefore, using distance formula,

→ Length of AB = √[(x2 - x1)² + (y2 - y1)²] = √[(4 - 0)² + (0 - 2)²] = √(4² + (-2)²) = √(16 + 4) = √20 = 2√5 units (Ans.)

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