Correct option is (D) 4 : 3
\(\because\) Any point on X-axis has y-coordinate zero.
Let line segment joining the points A(5, 4) and B(5, -3) divides X-axis at point C(x, 0) in the ratio k:1.
\(\therefore\) By section formula, the coordinates of point C is
\((x,0)=(\frac{5k+5}{k+1},\frac{-3k+4}{k+1})=(5,\frac{-3k+4}{k+1})\)
\(\therefore\) \(\frac{-3k+4}{k+1}=0\) (By comparing y-coordinate of point C)
\(\Rightarrow-3k+4=0\)
\(\Rightarrow k=\frac43\)
\(\Rightarrow\frac k1=\frac43\)
\(\therefore k:1=4:3\)
Hence, X-axis divides the line segment joining the points (5, 4) and (5, -3) in the ratio 4:3.
