In the given figure. line AB meets y-axis at point A. Line through C(2,10) and D intersects line AB at right angle at poiunt R find

(1) equation of line AB

(2) equation of line CD

(3) Co-ordinates of point E and D

#### Solution

(1) `"Slope of line AB "=m=(8-6)/(-6-0)=2/-6=-1/3`

The y-interoept of the line Ab is 6.

Thus , the equation of th given line is given by the slope -intercept from` y=mx+c`

i.e. `y=-1/3xx+6`

i.e.` 3y=-x+18`

i.e.` x+3y=18,` Which is the required equation.

(2) Since Ab and CD intersect at right angles,

`"slope"_(AB)xx "slope"_(CD)=-1`

`⇒ -1/3xx "slope"_(CD)=-1`

`⇒ Slope_(CD)=3`

U sing the slope-point from, the equation of CD is given by

`y-y_1=m(x-x_1)`

i.e. `y-10=3(x-2)`

i.e.` y-10=3x-6`

i.e. `3x-y+4=0` Which is the required equation of line CD.

(3) Since point E satisfies the equation Of AB, and the y-coordinate of E is 0, We can find the x-Coodinate of E.

`x+3(0)=18`

`⇒ x=18`

So, the coordinates of E are (18,0).

Now, since point D satisfies the equation Of CD, and the y-coordinate of D is 0, We can find the x-coordinate Of D.

`3x-(0)+4=0`

`⇒3x=-4`

`⇒x=-4/3`

So, the coordinates of D are `(-4/3,0)`