In what ratio is the segment joining (−1,−12) and (3,4) divided by the x-axis?

Let the x-axis divide the line segment joining A(−1,−12) and B(3,4) at point P(x,0) in the ratio k:1.
On the x-axis, the y-coordinate of any point is always 0.

Using the section formula for the y-coordinate:

y=
k+1
k⋅y
2
​
+1⋅y
1
​

​

Here, y
1
​
=−12, y
2
​
=4, and y=0:

0=
k+1
k(4)+1(−12)
​

0=4k−12
4k=12
k=3
Hence, the ratio k:1 is 3:1.