Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • The mid-point of the sides of a triangle are (1, 5, – 1), (0, 4, – 2) and (2, 3, 4). Find its vertices. Also find the centroid of the triangle.

The mid-point of the sides of a triangle are (1, 5, – 1), (0, 4, – 2) and (2, 3, 4). Find its vertices. Also find the centroid of the triangle.

Answers (1)

Given:

Mid-points of sides of triangle ABC are,

D(1,5,-1), E(0,4,-2) & F(2,3,4)

Let us assume that the vertices of the triangle are –

A(x1, y1, z1), B(x2, y2, z2) & C(x3, y3, z3).

Now, we know that E is the mid-point of AC, thus,

(x1 + x3/2, y1 + y3/2, z1 + z3/2) = (0,4,-2)

Thus,

C(x3, y3, z3) = C(-x1, 8 – y1, -4-z­1)

Now, mid-point of AB, F is

(x1 + x2/2, y1 + y2/2, z1 + z2/2) = (2,3,4)

Now, B(x2, y2, z2) = B(4-x1, 6-y1, 8-z1)

Now, mid-point of BC, D is,

-x1 + 4 – x1/2 = 1,

8 – y1 + 6 – y1/2 = 5

& - 4 – z1 + 8 – z1/2 = -1

Thus, x1 = 1, y1 = 2 & z1 = 3

Thus, A = (1,2,3), B = (3,4,5) & C = (-1,6,-7)

Now, for centroid,

G = (1+3-1/3,2+4+6/3, 3+5-7/3)

                  = (1,4,1/3)

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question