Question

in what ratio does y axis divides the line segment joining the points p(-4,5) and q(3,-7)? also find the coordinate of the points of intersection

Answer 1

Answer

The ratio does y axis divides the line segment joining the points p(-4,5) and q(3,-7) = 5 : 7

The coordinate of the points of intersection is (-13/12, 0)

Explanation

Let (x1,y1)= (-4,5) and (x2,y2) = (3,-7)

slope = (y2 -y1)/(x2 - x1) = (-7 - 5)/(3 - -4) = -12/7

Equation of the line pq  = (y-5)/(x--4) =-12/7

we get equation, 12x + 7y +13 = 0

Step 1: coordinate of the points of intersection

y coordinate = 0

To find x coordinate put the value of y = 0 in the equation

we get x= -13/12

coordinate of the points of intersection  =(-13/12, 0)

Step 2: Ratio does y axis divides the line segment joining the points p(-4,5) and q(3,-7)

Let (x, y) be the point in which divide a line  in the ratio p:q

let( x1, y1) and (x2, y2) be the two pints and w= p+q

point that divide the line in the ratio p: q is given by

x = x1 + p/w[x2 - x1]

Substituting we get p/w =5/12

Therefore p= 7 and q =12 - 5 = 7