Question

A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects x-axis at point A and y-axis at point B. M is the mid-point of the line segment AB. Find: 

1. the equation of the line. 
2. the co-ordinates of point A and B.
3. the co-ordinates of point M.

Answer 1

i. The equation of the line passing through the points P(–1, 4) and Q(5, –2) is 

`y - 4 = (-2 - 4)/(5 - (-1))[x - (-1)]`

i.e `y - 4 = (-6)/6(x + 1)`

i.e. y – 4 = –1(x + 1)

i.e. y – 4 = –x – 1

i.e x + y = 3

ii. The line x + y = 3 cuts x-axis at point A.

Hence, its y co-ordinate is 0.

And x co-ordinate is given by 

x + 0 = 3 `=>` x – 3 

So, the co-ordinates of A are (3, 0)

The line x + y = 3 cuts y-axis at point B.

Hence, its x co-ordinate is 0.

And y co-ordinates is given by 

0 + y = 3 `=>` y = 3 

So, the co-ordinates of B are (0, 3).

iii. Since M is the mid-point of line segment AB, 

So, co-ordinates of M = `((3 + 0)/2, (0 + 3)/2) = (3/2, 3/2)`