Find the perimeter of the rectangle whose coordinates are A (10, 10), B (10, 26), C (45, 26), D (45, 10)

The correct answer is: 102

The given rectangle is ABCD
The points are:
A = (10,10)
B = (10,26)
C = (45,26)
D = (45,10)
We can consider the length of any two adjacent sides.
Let AB be the length and BC be the breadth.
Let’s find the distance of the side AB
AB has x coordinate same. And the y coordinate has same sign. So the points are in the same quadrant.
We will find the absolute values of the points A and B. Absolute value is distance of the point from respective axis. Here x coordinate is same. So, absolute distance is from x axis.
Absolute distance of the point A is |10|
Absolute distance of the point B is |26|
As both of them are in same quadrant we will have to subtract their absolute distance to find the value of its length.
Length of AB = |26| - |10|
= 26 – 10
= 16 units.
Length of side AB is 16 units
Let’s find the distance of the side BC
BC has y coordinate same. And x coordinate has the same sign. So the points are in same quadrant.
We will find the absolute distance of the points B and C. Here y coordinate is same. So, we will measure distance from y axis.
Absolute distance of the point B is |10|
Absolute distance of the point C is |45|
As both of them are in same quadrant, we will have to subtract their absolute distances to find the value of its length
Length of BC = |45| - |10|
= 45 – 10
= 35 units
Length of side BC is 35 units.
We will find the perimeter now
Perimeter of rectangle ABCD = 2(length + breadth)
= 2(AB + BC)
= 2(35 + 16)
= 2(51)
= 102 units.
Therefore, perimeter of the rectangle ABCD is 102.

We can use distance formula to find the distance too. We have to be careful when finding the absolute values. We have to see which coordinates are same. And the signs of the coordinates.