Find the ratio in which the line segment joining A(1, – 5) and B(–

1.	Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.
Answer» Given , The LINE segment joining A(1, -5) and B(-4, 5) is divided by the x axis Let , the x axis divides the given line segment in the ratio m : n We know that , the section formula is given by $\boxed{ \sf{x = \frac{ mx_{2} + nx_{1}}{m + n} \: , \: y = \frac{ my_{2} + ny_{1}}{m + n} }}$ Thus , $\implies \tt 0 = \frac{ 5m - 5n}{m + n}$ $\implies \tt 0 = 5m - 5n$ $\implies \tt 5n = 5m$ $\implies \tt \frac{m}{n} = \frac{5}{5}$ $\implies \tt m : n = 1 : 1$ ★ The ratio in which x axis divides the given line segment is 1 : 1 Now , the coordinate of the point of division will be $\implies \tt x = \frac{ - 4(1) + 1(1)}{ 1 + 1}$ $\implies \tt x = \frac{ - 3}{2}$ ★ The point (-3/2 , 0) divides the given line segment