Question

What is the equation of the line that passes through the given point and is perpendicular to the given line?

Point: (1,1)
Line: y=1/5x+4/5

Answer 1

Explanation:

Hey there!

The equation of a line which passes through the point (1,1) is (y-1) = m1 (x-1)...............(i) {using one point formula}

Also, another equation which is perpendicular to the line is y = 1/5 x + 4/5..........(ii)

Comparing equation (ii) with y= mx+c, we get;

Slope (m2) = 1/5.

Now, As per the condition of perpendicular lines,

m1*m2 = -1

or, m1 * 1/2 = -1

or, m1= -2

Therefore, m1 = -2.

Keeping the value of m1 in equation (i) we get;

y-1 = -2(x-1)

y-1 = -2x+1

or, y+2x-2= 0

Therefore, the required equation is 2x+y-2= 0.

Hope it helps!