Write an equation of the perpendicular bisector of the line segment whose endpoints are (−1,1) and (7,−5)

The equation is

Explanation:

We have to first find the mid-point of the segment, the formula for which is

So, the midpoint will be

                                  =

It is the point at which the segment will be bisected.

Since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula

The slope is =

Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of   is

To write an equation, substitute the values in y = mx + c

WHere,

y = -1

x = 3

m = 3/2

Solving for c:

Thus, the equation becomes:

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.