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Question

In the given figure of cuboid if the coordinates of point E is (3, 2 ,1) and one of the corners as the origin.

How many of the following coordinates are correct?

A(0, 1, 0) B(3, 0, 1) C(3, 0, 0) D(2, 3, 0)

E(3, 2, 1) F(0, 2, 0) G(0, 2, 1) H(0, 0, 0)


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Solution

For a given point P in a space, we drop a perpendicular PM on the xz plane with M as a foot of perpendicular, then from the point M, we draw a perpendicular ML to the z-axis meeting it at the L. let OL be z, LM be x and MP be y. x, y and z are called the x, y and z coordinates respectively of the point P in the space. Coordinate of the point P are (x, y, z)

We will use the same concept to proceed.

Coordinates of point A

Point A lies on the z axis x & y coordinates must be zero.

z- coordinate is 1. Coordinates of point A are (0, 0, 1)

Coordinate of point B

Point B lies on the x – z plane, y-coordinates must be zero and the value of x and z- coordinate is 3 and 1.Coordinate of point B are (3, 0, 1)

Coordinate of point C

Point C lies on the x-axis y & z coordinate must be zero.

x coordinate is 3. Coordinate of point C are (3, 0, 0).

Coordinate of Point D

Point D lies on the x – y, plane, z-coordinate must be zero and the value of x and y- coordinate is 3 and 2. Coordinate of point D are (3, 2, 0).

Coordinates of point E

To reach E, we travel 3 units in the positive x direction and 2 and 1 units in the positive y and z direction. So the Coordinates of Point E will be (3, 2, 1).

Similarly, we get the coordinates of F and G equal to (0,2,0) and (0,2,1).

Coordinates of point H is (0, 0, 0) since it is the origin.

So, only 5 coordinates are correct


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