Question

if a[5,-1], b[-2,3] ,c[-4,-7] are vertices of triangle ABC and G is the centroid , find the area of triangle AGB

Answer 1

A=(5,-1) B=(-2,3) C=(-4,-7)

Therefore centroid

X=x+y+z÷3

X=-1÷3

Y=-5÷3

Area of triangle =

=11÷3

Answer 2

ANSWER:-

Area of ΔABC whose vertices are is

$(x_1,y_1),(x_2,y_2) \: and \: (x_3,y_3)are$

$Area \: of ΔABC = \frac{1}{2} [x_1(y_2,y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

In ΔABC, vertices are A(−5,7),B(−4,−5) and C(4,5)

$Area \: of \: triangle \: = \frac{1}{2} (- 5 (- 5 - 5 ) - 4(5 - 7) + 4(7 + 5))$

$= \frac{1}{2} ( - 50 + 8 + 48)$

$= 5 \: sq. \: units$

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