Line L has equation x + 2y - 10=0 and the line K, perpendicular to line L, passes through the origin
if the line L crosses the x axis at A and the y axis at B,
Find the coordinates of A and B and the coordinates of Q that divides AB in the ratio 2:3
the equation of Line L is x + 2y - 10 = 0. This line intersects the x and y axes at A and B respectively.
At point A, the y-coordinate is 0, the x-coordinate is 10. The point A is (10, 0). At point B, the x-coordinate is 0, the y coordinate is 5. The co-ordinates of B are (0, 5)
Point Q lies at a location such that AB is divided in the ratio 2:3.
The x-coordinate of Q is 10 - (2/5)*(10 - 0) = 6. The y-coordinate of Q is 0 - (2/5)*(0 - 5) = 2
The coordinate of point Q is (6, 2)
L : x+2y=10
at x axis ,y=0 thus coordinate of A(10,0)
at y axis ,x=0 thus coordinate of B(0,5)
Q divides AB in ratio of 2:3
Thus by section formula
`` Thus coordinate of Q(6,2).