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...

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

Asked on by seerboldly

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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)

aruv's profile pic

aruv | High School Teacher | (Level 2) Valedictorian

Posted on

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

`x=(3xx10+2xx0)/(3+2)=30/5=6`

`y=(3xx0+2xx5)/(3+2)=10/5=2`

`` Thus coordinate of Q(6,2).

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