Question

A line through origin meets the line x=3y+2 at right angles at point x find the coordinates of x

Answer 1

mark as brainliest answer...

Answer 2

Answer:

The coordinate of point x is $(\frac{1}{5},-\frac{3)}{5}$

Step-by-step explanation:

Any line passing through the origin is in the form y = mx, where m is the slope of the line.

Now, the given line is x = 3y +2

Writing this equation in slope intercept form y = mx +b

$x=3y+2\\3y=x-2\\\\y=\frac{1}{3}x-\frac{2}{3}$

Therefore, the slope of this given line is 1/3

Now, we use below concept:

The slopes of two perpendicular lines are negative reciprocal of each other.

Therefore, the slope of the line passing through origin is -3.

Hence, the equation is y = -3x

Now, in order to find the required point, we plug y = -3x in the given equation

$x=3(-3x)+2\\x=-9x+2\\10x=2\\\\x=\frac{1}{5}$

And y value is

$y=-3\cdot{1}{5}\\\\y=-\frac{3}{5}$

Therefore, the coordinate of point x is $(\frac{1}{5},-\frac{3)}{5}$