Question

The centroid of a rectangle bounded by the coordinate axes and the lines x=a y=b

Answer 1

The centroid of a rectangle bounded by the coordinate axes and the lines x=a y=b  is given by (a/2 , b/2)

Given:

• Rectangle bounded by the coordinate axes and the lines x=a, y=b

To Find:

• The centroid of the rectangle

Solution:

• Coordinate axes y = 0  and x = 0
• Centroid of Rectangle lies at intersection of Diagonals
• Diagonals of rectangle bisect each other hence intersects at mid point
• Mid Point formula for (x₁ , y₁ ) and (x₂ , y₂)  is   $(\dfrac{x_1+x_2}{2} ,\dfrac{y_1+y_2}{2})$

Step 1:

Find Intersection points of x=a , y=b , x = 0 and y = 0

(0 , 0) , (a , 0) , (a , b) , ( 0 , b)

Step 2:

Find Mid point of (0 , 0) and (a , b)   or (a , 0) and  ( 0 , b)

$(\dfrac{0+a}{2} ,\dfrac{0+b}{2})=(\dfrac{a}{2} ,\dfrac{b}{2})$

or

$(\dfrac{a+0}{2} ,\dfrac{0+b}{2})=(\dfrac{a}{2} ,\dfrac{b}{2})$

Hence, The centroid of a rectangle bounded by the coordinate axes and the lines x=a y=b  is given by (a/2 , b/2)