Coordinate Geometry: A Line Between 2 Points

Worked Solution

Dividing the equation p x + q y + r = 0 by q and re-arranging, we have

y = –

p q

x –

r q

which tells us that the gradient of AB is

–

p q

From the given coordinates, the gradient AB here is

By – Ay Bx – Ax

=

5 – (–6) (–1) – 4

=

–  11 5

= –

p q

so we let p be 11 and q be 5
The equation of the line is therefore of the form 11 x + 5 y + r = 0
Since the line goes through point A where x = 4 and y = –6,
putting these values into the equation of the line gives:
44 – 30 + r = 0 r = –14
The line AB is therefore 11 x + 5 y – 14 = 0 or any multiple of this equation.