If the mid point of the line segment joining the points A 3 4 and B k 6 is P x y and x y ndash 10 0 ...........

Mathematics (NDA) Coordinate Geometry

If the mid-point of the line segment joining the points A (3, 4) and B (k, 6) is P (x, y) and x + y – 10 = 0, find the value of k.

Mid-point of the line segment joining A (3, 4) and B (k, 6) = 3 46 , 2 2 + + k = 3 ,5 2 + k

Then, 3 ,5 2 + k = (x, y) Therefore, 3 2 + k = x and 5 = y.

Since x + y – 10 = 0, we have 3 2 + k + 5 – 10 = 0 i.e., 3 + k = 10

Therefore, k = 7

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