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**david****Guest**

Determine whether the point W(2,-1) lies on the perpendicular bisector of line segment UV, endpoints U(3,5) and V(-3,-1). Explain and justify your answer.

I cant figure it out, if someone could, it would be a pleasure!!!!!

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,503

Given two points, the equation of the line joining the points is

(y-y1)/(y2-y1) = (x-x1)/(x2-x1)

Substituting y1 = 5, y2 = -1, x1 = 3 and x2 = -3, the equation of the line is

x-y+2 = 0,

The slope of this line m=(y2-y1)/(x2-x1), i.e., m = 1.

The slope of a line perpendicular to this line would be -1

(Because, if two lines are perpendicular, the product of their slopes is -1).

The midpoint of U(3,5) and V(-3, -1) is given by

[(x1+x2)/2, (y1+y2)/2]

Therefore, the midpoint of the line UV is

(0,2).

The equation of a line of given slope passing through a given point is

(y-y1) = m(x-x1)

We know, m=-1 for the perpendicular line.

Therefore, the equation of the perpendicular bisector is

(y-2) = -1(x-0)

or

x+y-2 = 0

Substitute the x and y coordinates of point W(2,-1) in this equation.

We see that it does not satisfy the equation.

Therefore, the point does not lie on the perpendicular bisector.

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