Answer:
a) The coordinates of the missing vertex = (7, 8)
b) Area = 18 square units
Perimeter = 18 units
Step-by-step explanation:
a) We know three of the four vertices:
A: (4, 2) C ______ D(?)
B: (7, 2) | |
C: (4, 8) A |______| B
To find the coordinates of the missing vertex we need to calculate the distance in the x-direction from point A to point B:
[tex] B_{x} - A_{x} = 7 - 4 = 3 [/tex]
Hence, the distance of point D from point C in the x-direction is:
[tex] D_{x} = C_{x} + 3 = 4 + 3 = 7 [/tex]
Now, to find the coordinate in "y" we need to calculate the distance in the y-direction between point C and point A:
[tex] C_{y} - A_{y} = 8 - 2 = 6 [/tex]
Then, the distance of point D from point B in the y-direction is:
[tex] D_{y} = B_{y} + 6 = 2 + 6 = 8 [/tex]
Therefore, the coordinates of the missing vertex (point D) are:
[tex] D = (D_{x}, D_{y}) = (7, 8) [/tex]
b) The area of the rectangle is:
[tex] a = (B_{x} - A_{x})*(C_{y} - A_{y}) = 3*6 = 18 units^{2} [/tex]
The perimeter is given by:
[tex] p = 2*(3 + 6) = 18 units [/tex]
I hope it helps you!
