In what ratio is the line joining P(5, 3) and Q(-5, 3) divided by the x-axis? Also, find the co-ordinates of the point of intersection.

Let point on x-axis dividing PQ be (a, 0).

By section formula,

y = $\dfrac{m$1y2 + m2y1}{m1 + m2}

Substituting values we get :

$\Rightarrow 0 = \dfrac{m$1 \times 3 + m2 \times 3}{m1 + m2} \\[1em] \Rightarrow 0 = 3m1 + 3m2 \\[1em] \Rightarrow 3m1 = -3m2 \\[1em] \Rightarrow \dfrac{m1}{m2} = -\dfrac{3}{3} \\[1em] \Rightarrow \dfrac{m1}{m2} = -\dfrac{1}{1}

The negative ratio shows that the line PQ does not intersects with x-axis.

Hence, the x-axis does not intersect the line PQ, so no ratio or point of intersection exists.