Name the octants in which the following points lie: (1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (– 4, 2, –5), (– 4, 2, 5), (–3, –1, 6) (2, – 4, –7).

Asked by Abhisek | 11 months ago |  82

##### Solution :-

Consider the following table.

 Octants I II III IV V VI VII VIII x + - - + + - - + y + + - - + + - - z + + + + - - - -

By following rules given in the above table, we can conclude the following results.

Since, all the three coordinates in the point (1,2,3) are positive, so this point is in the octant I .

Since in the point (4,−2,3) , the x and z -coordinate are positive and the y - coordinate is negative, so this point is in the octant IV.

Since in the point (4,−2,−5) , the y and z -coordinate are negative and the x - coordinate is positive, so this point is in the octant VIII .

Since in the point (4,2,−5) , the x and y-coordinate are positive and the z - coordinate is negative, so this point is in the octant V.

Since in the point (−4,2,−5) , the x and z -coordinate are negative and the ycoordinate is positive, so this point is in the octant VI.

Since in the point (−3,−1,6) , the x and y-coordinate are negative and the z - coordinate is positive, so this point is in the octant II .

Since in the point (−2,−4,−7) , all the three coordinates in the point are negative, so this point is in the octant VII .

Answered by Pragya Singh | 11 months ago

### Related Questions

#### A(1, 2, 3), B(0, 4, 1), C(-1, -1, -3) are the vertices of a triangle ABC. Find the point in which the bisector of the

A(1, 2, 3), B(0, 4, 1), C(-1, -1, -3) are the vertices of a triangle ABC. Find the point in which the bisector of the angle ∠BAC meets BC.

#### The mid-points of the sides of a triangle ABC are given by (-2, 3, 5), (4, -1, 7) and (6, 5, 3). Find the coordinates

The mid-points of the sides of a triangle ABC are given by (-2, 3, 5), (4, -1, 7) and (6, 5, 3). Find the coordinates of A, B and C.

#### If the points A(3, 2, -4), B(9, 8, -10) and C(5, 4, -6) are collinear, find the ratio in which C divided AB.

If the points A(3, 2, -4), B(9, 8, -10) and C(5, 4, -6) are collinear, find the ratio in which C divided AB.