Question

The centroid of the triangle ABC is (2, 3) and
A= (4, 2), B = (4, 5), then the area of the triangle
ABC
(a) 6 (6) 9 (c) 8 (d) 5.​

Answer 1

Given,

Coordinate of the centroid of ∆ABC = (2,3)

Coordinate of A and B = (4,2) and (4,5)

To find,

Area of ∆ABC

Solution,

First of all, we have to calculate the coordinates of the third vertex of the ∆ABC. (Third vertex = Point C)

Let, the coordinates of point C = (x,y)

Now, the coordinates of the centroid :

= (4+4+x)/3 ,(2+5+y)/3

= (8+x)/3 ,(7+y)/3

According to the question,

(8+x)/3 = 2

8+x = 6

x = -2

(7+y)/3 = 3

7+y = 9

y = 2

Coordinate of point C = (-2,2)

Point A = (4,2) = X1,Y1

Point B = (4,5) = X2,Y2

Point C = (-2,2) = X3,Y3

Area of ∆ABC = ½×[ 4(5-2)+4(2-2)-2(2-5)]

= ½ (12+6)

= ½ (18)

= 9 square units

Hence, the area of triangle is 9 sq. units.