Question

The ordinate of a point lying on the line joining the points (6, 4) and (7, –5) is –23. Find the coordinates of that point.

Answer 1

Let A = (6, 4) and B = (7, –5)

Slope of the line AB = `(-5 - 4)/(7 - 6) =-9`

(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).