Question

Indicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5).

Answer 1

The correct answer is x+3y=-3

Explanation:

My fist step to solving this question would be to find the mid-point of the given line. The mid point of (4,1) and (2,-5) is (3,-2). The mid point is where the perpendicular bisector connects or bisects the given segment. My second step would be to graph the two given points and to connect them, forming a line. This way, I would know the slope of the line and then I would be able to find the slope of the perpendicular bisector, since the slope for perpendicular lines is the opposite reciprocal of the given line. In doing this, I discovered that the slope of the segment with the given endpoints is 3 which means that the slope of the perpendicular bisector will be x . So, so far we've got a point of intersection and a slope which is all we need to formulate the equation of the line that we are looking for.

In the end, our answer will be x+3y=-3

Answer 2

y = (-1/3)x - 3

Explanation

To get the equation of a line we need; gradient of that line and and a point that lies on that line.

Firstly, we find the midpoint to get the point that lies on the required equaion.

midpoint = ((4+2)/2 , (1+ -5)/2)

= (6/2, -4/2)

= (3, -2)

Secondly, we find the gradient of the line.

gradient = Δy/Δx

= (1- -5)/(4-2)

= 6/2

= 3

The products of gradients of perpendicular line is -1.

∴ m₁ ₓ m₂ = -1

3 ₓ m₂ =-1

m₂ = -1/3

Now that we have the gradient and the point, we can find the equation a follows:

-1/3 = (y - -2)/(x-3)

-1(x-3) = 3(y+2)

-x + 3 = 3y +6

3y = -x - 3

y = (-1/3)x - 3