A(1,7) B(6,4) and C(5,5) are three points in a plane 1. Find the equations of the perpendicular bisectors of AB and AC
Determine the point of intersection of the perpendicular bisectors in (I)

Step-by-step explanation:

Middle point of AB

x(m) = (6+1)/2 = 7/2

y(m) = (7+4)/2 = 11/2

slope of the line that contains AB

(4-7)/(6-1) = -3/5

eqaution of the perpendicular bisector

y-11/2 = 5/3(x-7/2)

y = 5/3x -35/6 + 11/2

y = 5/3x + (-35 + 33)/6

y = 5/3x -1/3

Middle point of AC

x(m) = (1+5)/2 = 3

y(m) = (7+5)/2 = 6

Slope of the line that contains AC

(5-7)/(5-1) = -1/2

equation of the perpendicular bisector

y-6 = 2(x-3)

y = 2x -6 + 6

y = 2x

Point of intersection

y= 5/3x -1/3

y = 2x

2x = 5/3x - 1/3

6x = 5x - 1

x = -1

y = -2

P(-1,-2)

(1,7)

Step-by-step explanation:

Given:

A(1,7)

B(6,4)

C(5,5)

Solution:

Mid point of AB = M((1+6)/2,(7+4)/2) = M(3.5,5.5)

Slope of AB = (4-7)/(6-1) = -3/5

Perpendicular bisector of AB:

L1: y -  11/2 = -(3/5)(x-7/2) (1)

Mid point of AC, m= N((1+5)/2,(7+5)/2) = N(3,6)

Slope of AC, n = (5-7)/(5-1) = -2/4 = -1/2

perpendicular bisector of AC:

L2: y-6 = -(1/2)(x-3) "(2)

To find the point of intersection,

(1)-(2)

-5.5 - (-6) = -(3/5)x +12/5 + x/2 - 3/2

1/2 = -x/10 + 6/10

x/10 = 1/10

x = 1

substitute x in (1)

y = 3/2+11/2 =7

Therefore Point of intersection is (1,7)

answer: a.

step-by-step explanation: the answer is a. because, you need to converge the fractions to find a solution.

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.