Question

If the mid-points of the sides of a triangle are (-2,5) , (2,4) and (-1,2). [3]

Find the coordinates of the vertices of the triangle​

Answer 1

Given : mid-points of the sides of a triangle are (-2,5) , (2,4) and (-1,2).

To Find :  the coordinates of the vertices of the triangle​

Solution:

Let say Vertex of Triangle A ( a , b)  , B (c , d)  and C ( e , f)

(-2 , 5)  mid point of AB

( 2 , 4) mid point of BC

(-1  , 2)  Mid point of AC

(a + c)/2  = - 2  => a + c  = - 4

( b + d) /2 = 5  => b + d  = 10

(c + e)/2 = 2  =>   c + e  = 4

(d + f)/2 = 4  => d  + f  = 8

(a + e)/2 = - 1 => a  + e  = - 2

(b + f)/2 = 2  =>  b  + f  =  4

a + c + c + e + a + e = -4 + 4 - 2

=> 2(a + c + e)  = - 2

=> a + c + e  =  - 1

a + c + e  =  - 1

a + c  = - 4

=> e = 3

   c = 1

    a =  - 5

b + d   + d + f + b + f  = 10 +  8 + 4

=> b + d + f  = 11

 b + d  = 10

=> f = 1

b = 3

d = 7

coordinates of the vertices of the triangle​

A ( - 5 , 3)

B ( 1 , 7)

C ( 3 , 1)

Learn more:

If P (-1,1) is the midpoint of the line segment joining A(-3,b) and B (1 ...

brainly.in/question/13203314

In a triangle ABD, C is the midpoint of BD. If AB=10, AD=12, AC=9 ...

brainly.in/question/13399658