Answer:
a + b = 12
Step-by-step explanation:
Given
Quadrilateral;
Vertices of (0,1), (3,4) (4,3) and (3,0)
Required
Let the vertices be represented with A,B,C,D such as
A = (0,1); B = (3,4); C = (4,3) and D = (3,0)
To calculate the actual perimeter, we need to first calculate the distance between the points;
Such that:
AB represents distance between point A and B
BC represents distance between point B and C
CD represents distance between point C and D
DA represents distance between point D and A
Calculating AB
Here, we consider A = (0,1); B = (3,4);
Distance is calculated as;
Substitute these values in the formula above
Calculating BC
Here, we consider B = (3,4); C = (4,3)
Here,
Substitute these values in the formula above
Calculating CD
Here, we consider C = (4,3); D = (3,0)
Here,
Substitute these values in the formula above
Lastly;
Calculating DA
Here, we consider C = (4,3); D = (3,0)
Here,
Substitute these values in the formula above
The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral
Recall that
This implies that
By comparison
Divide both sides by
By comparison
Divide both sides by
Hence,
a + b = 2 + 10
a + b = 12
