Find the perpendicular bisector of the points a(3,6) and b(-1,4). give your answer in the form
ax + by = c.

the equation of the perpendicular bisector of segment AB is y = -2x + 7

Step-by-step explanation:

Going from B(-1, 4) to A(3, 6), x increases by 4 and y increases by 2.  Thus, the slope of this line is m = rise / run = 2/4, or 1/2.

Any line perpendicular to the one joining A and B has a slope which is the negative reciprocal of 1/2:  that'd be -2.

                                                               3 - 1       6 + 4

The midpoint of line segment AB is ( , ), or (1, 5)

                                                                  2            2

Thus, the perpendicular bisector passes through the midpoint (1, 5) and has slope -2:

Starting from y = mx + b, we get  5 = -2(1) + b, or 7 = b, and so the equation of the perpendicular bisector of segment AB is

y = -2x + 7

angle uzt is congruent to angle tzy. angle vzw is congruent to angle yzx.

(credits to leowren)

step-by-step explanation: