Question

The co-ordinates of two points P and Q are (2, 6) and (−3, 5) respectively. Find:

1. the gradient of PQ;
2. the equation of PQ;
3. the co-ordinates of the point where PQ intersects the x-axis.

Answer 1

Given, co-ordinates of two points P and Q are (2, 6) and (–3, 5) respectively.

i. Gradient of PQ = `(5 - 6)/(-3 - 2) = (-1)/(-5) = 1/5`

ii. The equation of the line PQ is given by:

y − y₁ = m(x − x₁)

`y - 6 = 1/5(x - 2)`

5y − 30 = x − 2

5y = x + 28

iii. Let the line PQ intersects the x-axis at point A(x, 0).

Putting y = 0 in the equation of the line PQ, we get,

0 = x + 28

x = −28

Thus, the co-ordinates of the point where PQ intersects the x-axis are A(−28, 0).