Mathematics
Easy

Question

# Calculate the area of the rectangle whose coordinates are A (-45, -16), B (-45, -5), C (-8, -5), D (-8, -16)

## 96 sq. units    120 sq. units    407 sq. units    128 sq. units Hint:

## The correct answer is: 407 sq. units

### The coordinates of the rectangle ABCD areA 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 lengthThe points A,B,C and D have same signs of coordinates. So, they are in same quadrant.We will consider the side AB as length and BC as breadthWe 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= 11Length 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= 37Breadth of the rectangle is 36 units.The formula for area is (length × breadth)Area of rectangle ABCD = (length × breadth)= (11 × 37)= 407 sq. unitsTherefore, area of the rectangle is 407 sq. units.

For such questions, we have to see if the points of the rectangle are in same quadrant or adjacent quadrants. For points in adjacent quadrants, we have to add the absolute values. We can use distance formula to find the length of sides of rectangle too.

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