Question

if the centroid of a triangle is(1,4) and the vertices are(4,-3) and(-9,7)then the area of

Answer 1

Answer:

here is your answer

183² / 4 units

Step-by-step explanation:

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Answer 2

Answer:

The area of the triangle is $\frac{183}{2}$.

Step-by-step explanation:

Let the one vertex be (x,y).

Given, the centroid of the triangle  = (1,4)

other points are (4,-3) & (-9,7)

The co-ordinates of the centroid of triangle of vertices A(x1, y1), B(x2,y2), C(x3,y3) is ( $\frac{x1 + x2 + x3}{3}$ , $\frac{y1 + y2 + y3}{3}$ ).

So,

(1,4) = ( $\frac{x + 4 - 9}{3}$ , $\frac{y - 3 + 7}{3}$ )

Comparing the terms from both sides,

⇒ 1 = (x + 4 - 9)/3

⇒ x = 8

and

⇒ 4 = (y + 4)/3

⇒ y = 8

So, the coordinate of the third vertex is (8,8).

Then, the area of a triangle if all the vertices are non-collinear points

ar(ΔABC) = $\frac{1}{2}$ Ιx1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)Ι

ar(ΔABC) = $\frac{1}{2}$ Ι4(7 - 8) - 9(8 + 3) + 8(-3 - 7)Ι

ar(ΔABC) = $\frac{1}{2}$ Ι- 4 - 99 - 80Ι

ar(ΔABC) = $\frac{183}{2}$.

Hence, the area of the triangle is 91.5.

To know more about centroid, click on the link below:

https://brainly.in/question/8570384

To know more about non-collinear points, click on the link below:

https://brainly.in/question/12356785

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