Question

The mid- Point of the sides of a triangle are(1, 5, -1), (0, 4,-2) & (2, 3, 4). Find the vertices.​

Answer 1

Answer:

$\bold\red{(3,4,4)\:,\:(-1,6,-6)\:and\:(1,2,4)}$

Step-by-step explanation:

Let the coordinate of vertices of triangle ABC be

A(a,b,c)

B(x,y,z)

C(p,q,r)

Let,

the mid point of AB be (1,5,-1)

the mid point of BC be (0,4,-2)

the mid point of AC be (2, 3, 4)

Therefore,

From mid point formula,

we get,

a + x = 2 ....... (i)

b + y = 10 .........(ii)

c + z = -2 ..........(iii)

a + p = 4 ...........(iv)

b + q = 6 .............(v)

c + r = 8 .............(vi)

x + p = 0 .............(vii)

y + q = 8 .............(viii)

z + r = -2 ..............(ix)

Solving all the Equation,

we get,

$a = 3 \\ \\ b = 4 \\ \\ c = 4 \\ \\ p = 1 \\ \\ q = 2 \\ \\ r = 4 \\ \\ x = - 1 \\ \\ y = 6 \\ \\ z = - 6$

Hence,

the coordinates of triangle ABC are

A (3,4,4)

B (-1,6,-6)

C (1,2,4)