Given a(2,0) and b(8,4), show that p(3,5) is on the perpendicular bisector of line ab by these 2 methods 1)show line ab is perpendicular to pm where m is the midpoint of line ab 2) show pa is equal to pb

Gradient of AB is 4 - 0 / 8 - 2 = 4/6 = 2/3

Gradient of PM is -1 divide by 2/3 = -3/2

Solution for (1):

The midpoint of AB , M, is (2,0) + 1/2(8 - 2, 4 - 0)

(2,0) + (3,2) = 5,2

The gradient of PM then is (5 - 2) / (3 - 5) = -3/2

Therefore AB is perpendicular to PM since gradient of two perpendicular bisectors is -1

Solution for (2):

AM^2 + PM^2 = PA^2 , PM^2 + MB^2 = PB^2

AM^2 + PM^2 must be equal to PM^2 + MB^2

and since PM passes through the middle of AB then;

PA^2 = PB^2

(Finding the square root)

PA = PB

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.

answer: 8

step-by-step explanation: if you add the possibilities 5 different flavor and 3 different sizes 5+3=8