Question

4x+3y+12=0 straight line intersect by x and y axis. So, what's the midpoint coordinates?​

Answer 1

Answer:

First let us recall that if a straight line joining the points A(x1,y1) and B(x2,y2) is divided internally at the point P in the ratio m:n , then the coordinates of P will be (mx2+nx1m+n,my2+ny1m+n)...(1)

Now, the line 4x+3y+k=0 intersects the x axis at A and y axis at B. So, the coordinates of A & B are (−k4,0) and (0,−k3) respectively.

So, from (1) the coordinates of P at which the line AB is divided internally in the ratio 2:1 will be (2∗0+1∗−k42+1,2∗−k3+1∗02+1)=(−k12,−2k9)