Question

Q.19) In what Ratio is the
straight line joining the points (
2,15) and (8,9) divided by x-
axis:
O 5:3 internally
O 5:3 externally
O 1:4 externally
O 1:4 Internally​

Answer 1

Answer

Step-by-step explanation:

Answer 2

Find the ratio that x- axis divides the given line in.

Explanation:  

• The equation of a line joining two points having co-ordinates $(x_1,y_1),\ (x_2,y_2)$ is given by ,   $y-y_1=(\frac{y_2-y_1}{x_2-x_1} )(x-x_1)$    
• here we have two points $(2,15),\ (8,9)$ hence the line joining them is ,                $y-15=(\frac{9-15}{8-2} )(x-2) \\-> y=17-x$        ----(a)
• To find the point at which x-axis divides the line we put   $y=0$ in (a) we get, $x=17$
• hence, we get the point $(17,0)$ dividing the line joining $(2,15)\ (8,9)$
• let the ratio in which the x- axis divides the line be m:n then we have,                   $\frac {2m+8n}{m+n}=17 ,\ \ \ \ \ \ \frac{15m+9n}{m+n}=0 \\->15m+9n=0\\->\frac{n}{m}=-\frac{5}{3}$
• The x-axis divides the line in the ratio $5:3$ externally.