Question

if two vertices of a triangle are (5,6) and (-1,4) and its centroid is (2,3) then the area of triangle is​

Answer 1

Answer:

64 square units

Step-by-step explanation:

given 2 vertices and centroid

let the 3rd vertex be (x,y)

from these

5+(-1)+x =2

5-1+x=2

x=2-4

x=-2

on the other hand

6+4+y=3

10+y=3

y=-7

the 3rd vertex is (-2,-7)

from this we can find area

Answer 2

Answer:

The area of $\triangle ABC$ is 18sq.units.

Step-by-step explanation:

Let the vertices of given triangle be A(5,6) and B(-1,4) and let the third vertex be C and let the centroid be G(2,3).

To find the area of $\triangle ABC$ we shall use the property of triangles from co-ordinate geometry.

The area of a triangle formed by centroid and two vertices is one third of the area of actual triangle.Mathematically we write it as

$ar(\triangle GAB)=\frac{ar(\triangle ABC)}{3}= > ar(\triangle ABC)=3ar(\triangle GAB)}$

The area of the $\triangle GAB$ is found as follows

$A=\frac{1}{2}\left|\begin{array}{ccc}2&3&1\\5&6&1\\-1&4&1\end{array}\right|\\=\frac{1}{2}[2(6-4)-3(5+1)+1(20+6)]=\frac{12}{2} =6sq.units$

Hence the area of $\triangle ABC$ will be

$ar(\triangle ABC)=3\times6=18sq.units$

Therefore,

The area of $\triangle ABC$ is 18sq.units.

#SPJ2