Question

Point A lies on the line segment XY joining X(6,-6) and Y(-4,-1) in such a way that XA/XY=2/5 . If A lies on the line 3x+k(y+1)=0. Find the value of k

Answer 1

Answer:

k = 2  

using section formula:  

[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}

substitute the values m1 = 2 , x2= -4 , m2 = 3 , y2 = -1, y1 = -6 in the formula

= $\frac{-8+18}{5}$ , $\frac{-2-18}{5}$

= [ 2, -5] = coordinates of a  

now substitute in the equation 3x+ k(y+1)= 0  

3(2)+k(-4+1)=0

6+k(-3)=0

k=$\frac{-6}{-3}$

k=2  

hope it is helpful