Question

Angl is a square. The equation of line NG is Y= 1/2 X - 6. Find the equation of line LG in slope intercept form given that the coordinates of L are (-5,1)

Answer 1

Answer: y=-2x-9

Explanation:

If ANGL is a square, then NG and LG are adjacent sides.

Adjacent sides are perpendicular. [Each angle is 90°]

The equation of line NG is
`Y=\frac12 X-6`.

By comparing it to equation in slope intercept form y=mx+c ( where , m= slope , c=y-interecpt)

slope =
`\frac12`

Let slope of LG be n, then

`n* (1)/(2)=-1` [Product of slopes of two perpendicular line =-1]

`\Rightarrow n=-2`

Equation of a line passes through (a,b) and have slope m is given by :-

`(y-b)=m(x-a)`

Equation of LG :

`(y-1)=-2(x-(-5))\\\\\Rightarrow\ y-1=-2x-10\\\\\Rightarrow\ y=-2x-9` [In intercept form]