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Question
Point M (2, b) is the mid-point of the line segment joining points P (a, 7) and Q (6, 5). Find the values of ‘a’ and ‘b’.
Solution
Mid point formula = `((x_1 + x_2)/2, (y_1 + y_2)/2)`
Let P = (a, 7) = (x1, y1)
Q = (6, 5) = (x2, y2)
∴ (2, b) = `(("a" + 6)/2, (7 + 5)/2)`
∴ `2 = ("a" + 6)/2` and b = `12/2`
⇒ 4 = a + 6 and b = 6
⇒ a = - 2
∴ a = - 2, b = 6
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