Question

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.

Answer 1

Let A = (6, 4) and B = (7, -5)

Slope of the line AB =

(x₁, y₁) = (6, 4)

The equation of the line AB is given by

y - y₁ = m(x - x₁)

y - 4 = -9(x - 6)

y - 4 = -9x + 54

9x + y = 58 ...(1)

Now, given that the ordinate of the required point is -23.

Putting y = -23 in (1), we get,

9x - 23 = 58

9x = 81

x = 9

Thus, the co-ordinates of the required point is (9, -23).