Question

Find the ratio in which y-axis divides the line segment joining the points A(5, -6), and B (-1, -4). Also find the coordinates of the point of division.

Answer 1

Something like this

Explanation:

distance √(-1 - 5)² + (-6 - -4)² = √36 + 4 = √40 = 6.32

slope = 2/-6 = -1/3

distance (-1,-4) to (0, -4.63)

√(-1 - 0)² + (-4 - -4.63...)² = √1.4 = 1.18

6.32 - 1.18 = 5.14

1.18 : 5.14

Answer 2

ratio 5:1

coordinates (0,-13/3)

Explanation:

let any point on y-axis (0,y) divides the join of A(5,-6) and B(-1,-4) in the ratio k:1

`0=(-1(k)+1(5))/(k+1) \\or~0=-k+5\\or~ k=5\\\therefore ~y-axis~ divides ~A,B~in~the~ratio~5:1\\y=(5(-4)+1(-6))/(5+1) =(-26)/(6) =-(13)/(3)`

so coordinates of point of intersection are (0,-13/3)