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Sagot :
You have a triangle and to calculate its perimeter first you need to calculate the length of each side. Its sides are the segments AB, BC and AC and to obtain their lengths you have to substract one of its extreme from the other.
For example for segment AB
A - B = ( 1 , 1 ) - ( 1 , 4 ) = ( 1 - 1 , 1 - 4 ) = ( 0 , -3 )
Once you make the substraction you have a new point that defines a segment that has its origin in ( 0 , 0 ) and its end in the new point, in this case ( 0 , -3 ).
Its length is the same as segment AB and its given by the square root of the sum of the squares of its x and y coordinate:
[tex]\sqrt[]{0^2+(-3)^2}=\sqrt[]{9}=3[/tex]Now we have to do the same for segments BC and AC:
B - C = ( 1 , 4 ) - ( 5 , 1 ) = ( 1 - 5 , 4 - 1 ) = ( -4 , 3 )
And its length is:
[tex]\sqrt[]{(-4)^2+3^2}=\sqrt[]{16+9}=\sqrt[]{25}=5[/tex]A - C = ( 1 , 1 ) - ( 5 , 1 ) = ( 1 - 5 , 1 - 1 ) = ( -4 , 0 )
[tex]\sqrt[]{(-4)^2+0^2}=\sqrt[]{16}=4[/tex]And the perimeter of the triangle is therefore the sum of this three lengths:
Perimeter = 3 + 5 + 4 = 12
So the correct answer is A
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