# Calculate the perimeter of triangle ABC. A(1,1) , B(0,3) , C(1,-1)

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### 4 Answers

A(1, 1) B(0, 3) C(1, -1)

First we will calculate the measure of the sides:

AB = sqrt[(0-1)^2 + (3-1)^2]

= sqrt( 1 + 4)

= sqrt(5)

BC = sqrt[(1-0)^2 + (-1-3)^2]

= sqrt(1+ 16)

= sqrt(17)

AC = sqrt[(1-1)^2 + (-1-1)^2]

= sqrt(0+ 4)

= sqrt4 = 2

Then the perimeter is:

P = AB + BC + AC

= sqrt5 + sqrt17 + 2

The perimeter of a triangle is the sum of the lengths of the sides of the triangle.

Because we don't have the lengths of the sides of the triangle, we'll have to calculate them.

The formula for calculating the length of the side AB is:

AB = sqrt [(xB-xA)^2 + (yB-yA)^2]

AB = sqrt [(0-1)^2+(3-1)^2]

AB = sqrt(1+4)

AB = sqrt 5

AC = sqrt [(xC-xA)^2 + (yC-yA)^2]

AC = sqrt [(1-1)^2 + (-1-1)^2]

AC = sqrt 4

AC = 2

BC = sqrt [(xC-xB)^2 + (yC-yB)^2]

BC = sqrt [(1-0)^2 + (-1-3)^2]

BC = sqrt (17)

P = AB+AC+BC

**P = sqrt 5 + 2 + sqrt 17**

The distance between the point (x1,y1) and (x2,y2) is given as

sqrt [(x2-x1)^2 + (y2-y1)^2].

For the points:

- A and B

Length of AB is sqrt [(0-1)^2 + (3-1)^2]

=sqrt [1+4]= sqrt 5

- B and C

Length of BC is sqrt [(1-0)^2 + (-1-3)^2]

=sqrt [1^2 + 4^2]= sqrt 17

- C and A

Length of CA is sqrt [(1-1)^2 + (-1-1)^2]

=sqrt [0 + 4]=2

**Therefore the perimeter is 2 + sqrt 5 + sqrt 17**

The perimeter of the triangle ABC = AB+BC+CA.

A(1,1) , B(0,3) , C(1,-1)

We know that the distance d between the the points (x1,y1) and x2,y2) is given by:

d = sqrt{(x2-x1)^2+y2-y1)^2}

AB = sqrt((0-1)^2+(3-1)^2} = sqrt(1+2^2 ) = sqrt5.

BC= sqrt{(1-0)^2+(-1-3)^2} = sqrt(1+(-4)^2} = sqrt17.

CA = sqrt{(1-1)^2+(1- -1)^2} = sqrt 4 = 2.

Therefore Perimeter of the triangle ABC = sqrt5+sqrt17 +2 = 8.26 units.