Question

Find the ratio in which the line segment joining the point A(3,-3) and B(-2,7) is divided by x axis Also,find the co-ordinates of the point of division

Answer 1

Let the required ratio is k : 1 and the coordinate of point of division is (x , 0)

Given points of line segment are: A(3, -3) and B(-2, 7)

Now, (x , 0) = {(-2*k + 3*1)/(k+1), (7*k + (-3)*1)/(k+1)}

=> (x , 0) = {(-2k + 3)/(k+1), (7k - 3)/(k+1)} ..............1

Now (7k - 3)/(k+1) = 0

=> 7k - 3 = 0

=> k = 3/7

So, the ratio is 3/7 : 1 = 3 : 7

Again from equation 1, we get

    (x , 0) = {(-2 * 3/7 + 3)/(3/7 + 1), 0}

=> (x , 0) = {(-6/7 + 3)/(3/7 + 1), 0}

=> (x , 0) = {(-6 + 3*7)/(3 + 7), 0}

=> (x , 0) = {(-6 + 21)/10, 0}

=> (x , 0) = (15/10, 0}

=> (x , 0) = (3/2, 0}

thanks