Question

Find the co-ordinates of vertex C of triangle ABC, where A(4, 5), B(1, 2) and coordinates of its centroid are (3, 3).​

Answer 1

Answer:

c=(4,-1)

Step-by-step explanation:

let the given triangle be ABC ,given

A=(4,5) ,B=( 1,2)  and let C =(X,Y)

ALSO CENTROID G=( 3,3)

WE KNOW THAT CENTROID =(sum of x coordinates of vertices/3,sum of y coordinates of vertices /3)

then,

(3,3)=(4+1+X/3,5+2+Y/3)

BY SOLVING

X=4  ANDY=  -1  i.e, C=(4,-1)

Answer 2

Concept:

The centroid is the center point in the triangle where all the medians intersect.

Given:

Coordinates of Point A (4, 5), and

Coordinates of Point B (1, 2)

And,

Coordinates of centroid = (3, 3)

Find:

We are asked to find the coordinates of vertex C of triangle ABC.

Solution:

We have,

Coordinates of Point A = (4, 5) = (x₁, y₁), and

Coordinates of Point B = (1, 2) = (x₂, y₂)

And,

Coordinates of centroid = (3, 3)

Now,

Let,

Coordinates of vertex C = (x₃, y₃)

So,

We know that

Coordinates of Centroid of triangle = [(x₁ + x₂ + x₃) / 3 , (y₁ + y₂ + y₃) / 3]

Now,

(3, 3) = [(4 + 1 + x₃) / 3 , (5 + 2 + y₃) / 3]

So,

⇒

(4 + 1 + x₃) / 3 =  3   and (5 + 2 + y₃) / 3 = 3

Now,

Solve for x₃,

i.e.

(4 + 1 + x₃) / 3 =  3

⇒

5 + x₃ = 9

x₃ = 4

Now,

Solve for y₃,

i.e.

(5 + 2 + y₃) / 3 = 3

⇒

7 + y₃ = 9

y₃ = 2

So,

Coordinates of vertex C = (4, 2)

Hence, the coordinates of vertex C of triangle ABC are (4, 2).

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