Line segment XY has endpoints X(5,7) and Y(-3,3)

y=-2x+7

Step-by-step explanation:

line segment xy has endpoints x(5 7) and y(-3 3)

for the equation of the perpendicular bisector of line segment xy

slope of line segment xy = 7-3 / 5+3

= 4/8

=1/2

so slope of perpendicular bisector is -2

as m1m2= -1 or m1= -1/m2

As perpendicular bisector goes through midpoint of xy , let's find midpoint of xy

midpoint(x,y) = (5-3 / 2 , 7+3 / 2)

=(2/2, 10/2)

=(1,5)

find the equation of line(perpendicular bisector) passing through (1,5) and the slope -2

y-5 = -2(x-1)

y-5 =-2x+2

y=-2x+7

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.