Tes: Introduction To 3D Geometry - Commerce MCQ

In the 3D, fourth quadrant has x positive, y negative and z positive.

The image of(-2,3,4) reflects in the 1st quadrant. As we know that in 1st quadrant all the x,y and z are positive 
So the resultant will be : (2,3,4)

The x-axis and y-axis taken together determine a plane known as XY-plane.

The eight octants can be divided into 2 parts.
Positive direction of Z-axis and negative direction of Z-axis.
Thus we have 2 sets of co-ordinates:
(+, +, +) ; (+, -, +) ; (-, +, +) ; (-, -, +)
(+, +, -) ; (+, -, -) ; (-, +, -) ;  (-, -, -)
Therefore, the points (1,-2,-3) lies in 8th octant.

If a point is on the x-axis, then its y-coordinates and z-coordinates are zero.

In this question, the ��-coordinate is negative three, the ��-coordinate is negative six, and the ��-coordinate is zero. As �� is equal to zero, the point will not move in the direction of the ��-axis. We can therefore conclude that as �� is equal to zero, the point will lie on the ����-plane. If our ��-coordinate was equal to zero but �� and �� had a positive or negative value, the point would lie in the ����-plane.

The point O is called the origin of the coordinate system. The three coordinate planes divide the space into eight parts known as octants. These octants could be named as XOYZ, X′OYZ, X′OY′Z, XOY′Z, XOYZ′, X′OYZ′, X′OY′Z′ and XOY′Z′.

Given: Point is (5, 2, -7)
To find: the image of the point in xy-plane

Since we need to find its image in xy-plane, a sign of its z-coordinate will change
So, Image of point (5, 2, -7) is (5, 2, 7)

L is the foot of the perpendicular from (3, 4, 5) to the X-axis. It will have Y and Z- coordinate as 0.
L (3, 0, 0)