Mathematics
The ordinate of a point lying on the line joining the points (6, 4) and (7, -5) is -23. Find the co-ordinates of that point.
Straight Line Eq
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Answer
Let point A = (6, 4) and B = (7, -5).
Let the point P be (a, -23).
By formula,
Slope =
Slope of AB = = -9.
By point-slope form,
⇒ y - y1 = m(x - x1)
⇒ y - 4 = -9(x - 6)
⇒ y - 4 = -9x + 54
⇒ 9x + y = 54 + 4
⇒ 9x + y = 58.
Since, P lies on AB so it will satisfy the equation.
Substituting values of P in equation we get,
⇒ 9(a) + (-23) = 58
⇒ 9a - 23 = 58
⇒ 9a = 58 + 23
⇒ 9a = 81
⇒ a =
⇒ a = 9.
∴ P = (a, -23) = (9, -23).
Hence, co-ordinates of the required point are (9, -23).
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