Question

The centroid of a triangle is (1,4) and the coordinates of its vertices are (4,-3) and (-9,7). find the area of triangle

Answer 1

given

(x1,x1)=(4,-3)

(x2,y2)=(-9,7)

c(x,y)=(1,4)

c(x.y)=(x1+x2+x3/3,y1+y2+y3/3)

(1,4)=(4-9+x3/3,-3+7+y3/3)

(1,4)=(-5+x3/3,4+y3/3)

equate with respect to x and y

1=--5+x3/3

3=-5+x3

x3=8

similarly

4=4+y3/3

12=4+y3

y3=8

we get (x3,y3)=(8,8)

area of triangle is

=1/2[(x1.y2+x2.y3+x3.y1)-(x2.y1+y2x3+y3.x1)]

=1/2[(-36-72-24)-(27+56+32)]

=1/2[(-132)-(115)]

=1/2[-247]

=123.5 (negative sign is neglected)

if any mistakes sorry!!

Answer 2

Answer:

the answer is -183/2 but area cannot be negative, so answer is 183/2 sq units

Step-by-step explanation:

Here, we have to find the area of the triangle, for that, we need the coordinate of all the three vertices of the triangle but here one is missing, so we have to find the coordinate of that missing vertex.

Let us assume that vertex as (x1,y1)

I hope you have studied the centroid formula that is as follows:

C(x,y)= C[(x1+x2+x3)/3 , (y1+y2+y3)/3]

C(1,4)=[(x+4-9)/3 , (y+7-3)/3]

=>(x-5)/3=1  and (y+4)/3=4

=>x-5=3 and y+4=12

=>x=8 and y =8

hey! we got the vertex (x1,y1) that is (8,16)

Now, I hope you have studied how to find the area of a triangle when coordinates of all vertex are given.

Area of a triangle=(1/2) [x1 (y2 – y3 ) + x2 (y3 – y1 ) + x3(y1 – y2)]

here, we are going to take,

x1=8 y1=8

x2=4 y2=-3

x3=-9 y3=7

now simply put the values in (1/2) [x1 (y2 – y3 ) + x2 (y3 – y1 ) + x3(y1 – y2)], you will get your answer.

You can do it yourself, isn't it?