Question

Find the ratio in which the line joining (-5,1) and (1,-3) divides the line joining (3,4) and (7,8). Also find the coordinates of the point of intersection.​

Answer 1

Answer:

Step-by-step explanation:Let x= 2 divide the line joining A (5,6) and B(-3,4) at the point P in the ratio k:1. Clearly P = (2, y) for some y-coordinate y.

Applying section formula viz., {(mx2+nx1)/(m+n), (my2+ny1)/(m+n)} for P we have (2,y) ={ (-3k+5)/(k+1), (4k+6)/(k+1)}……(1) Equating the x- coordinates both sides we have 2= (-3k+5)/(k+1) => 2k+2 = -3k+5 => k = 3/5.

Hence the line joining A(5,6) and B(-3,4) is divided by P or the line x=2 in the ratio 3/5 : 1 or 3 : 5.

To find the y-coordinate, equate the y- coordinates of (1) and noting k= 3/5. We then have y = {4(3/5) + 6}/{(3/5)+1} = 21/4.

Hence the point of intersection of the line joining A (5,6) and B(-3,4) and the line x=2 is P(2, 21/4