Write an equation of the perpendicular bisector of the segment with the endpoints (8,10) and ( -4,2). y =

The equation of the perpendicular bisection that passes through the point (2,6) and has a slope -3/2 is and this can be determined by using the point-slope form of the line.

Given :

Endpoints  -- (8,10) and (-4,2)

The following steps can be used in order to determine the equation of the perpendicular bisector:

Step 1 - First, determine the slope of the line that passes through points (8,10) and (-4,2).

Step 2 - So, the slope of the perpendicular bisector is given by:

Step 3 - Now, determine the midpoint of the line that passes through the points (8,10) and (-4,2).

Step 4 - So, the equation of the perpendicular bisection that passes through the point (2,6) and has a slope -3/2 is:

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link

The required equation is:

Step-by-step explanation:

To find the equation of a line, the slope and y-intercept is required.

The slope can be found by finding the slope of given line segment. A the perpendicular bisector of a line is perpendicular to the given line, the product of their slopes will be -1 and it will pass through the mid-point of given line segment.

Given points are:

We will find the slope of given line segment first

Let m_1 be the slope of perpendicular bisector then,

Now the mid-point

We have to find equation of a line with slope -3/2 passing through (2,6)

The equation of line in slope-intercept form is given by:

Putting the value of slope

Putting the point (2,6) to find the y-intercept

The equation is: