Find the perimeter of the rectangle whose coordinates are A (-45, -16), B (-45, -5), C (-8, -5), D (-8, -16)

The correct answer is: 96

The coordinates of the rectangle ABCD are
A is (-45,-16)
B is (-45,-5)
C is (-8,-5)
D is (-8,-16)
We have to find the length of the adjacent sides.
To find the length we will use the following criteria:
1) If x coordinate is same, we will find the absolute distance using y coordinate. An absolute distance is the length of the point from the respective axis. If x coordinate is same then its length is measured from x axis. It is a positive quantity.
2) If y coordinate is same we will use the x coordinate to find absolute distance.
3) If the points are in same quadrant, we will have to subtract the absolute distances to find length.
4) If the points are in adjacent quadrants, we will have to add the absolute distances to find length.
As all the points have same sign, they are in same quadrant.
We will consider the side AB as length and BC as breadth.
We will find the length of side AB.
For the points A and B, x coordinate is same. We will find the absolute distance using y coordinate. It is distance from x axis.
Absolute distance of the point A = |-16|
Absolute distance of the point B = |-5|
Length of AB = |16| - |-5|
= 16 – 5
= 11
Length of the rectangle is 11 units.
We will find the length of side BC.
For the points B and C, y coordinate is same. We will find the absolute distance using x coordinate. It is distance from y axis.
Absolute distance of the point B = | -45|
Absolute distance of the point C = |-8|
Length of BC = |-45| - |-8|
= 45 - 8
= 37
Breadth of the rectangle is 37 units.
The formula for area is 2(length + breadth)
Area of rectangle ABCD = 2(length + breadth)
= 2(11+ 37)
= 96 units
Therefore, area of the rectangle is 96 units.

For such questions, we have to be careful about the coordinates of the rectangle. We can use distance formula to find the distance too.