# 3d Graph Worksheet

3d Graph Worksheet
• Page 1
1.
Find the coordinates of the point P shown.

 a. (0, 0, 4) b. (4, 0, 0) c. (0, 4, 0) d. (0, - 4, 0)

#### Solution:

P is a point on the y - axis 4 units left of origin O
[Refer the figure.]

So, the coordinates of P are (0, - 4, 0)
[Use negative sign for left side.]

2.
What are the coordinates of the point A?

 a. (1, - 2, 3) b. (1, 2, 3) c. (- 1, 2, 3) d. (1, 2, - 3)

#### Solution:

The point A is 1 unit forward of origin, so its x - coordinate is 1.
[Refer the figure.]

The point A is 2 units right of origin, so its y - coordinate is 2.
[Refer the figure.]

The point A is 3 units upwards of origin, so its z - coordinate is 3.

So, the coordinates of A are (1, 2, 3).

3.
Find the coordinates of the point B shown.

 a. (3, - 3, 5) b. (3, 3, -5) c. (3, - 3, - 5) d. (3, 3, 5)

#### Solution:

The point B is 3 units forward of origin, so its x - coordinate is +3.
[Refer the figure.]

The point B is 3 units left of origin, so its y - coordinate is - 3.

The point B is 5 units downward of origin, so its z -coordinate is - 5.
[Refer the figure.]

So, the coordinates of the point B are (3, - 3, - 5).

4.
What does the graph of $\mathrm{ax + by + cz + d}$ = 0 represent?
 a. A plane b. A line c. A point d. A circle

#### Solution:

The general first degree equation ax + by + cz + d = 0 where a, b, c not become zero at a time represents a plane.

5.
A line that passes through two intercepts of a plane on the coordinate axes is called
 a. A segment b. Axis c. A trace d. An intercept

#### Solution:

A line that passes through two intercepts of a plane on the coordinates axes is called a trace of it.
[Definition.]

6.
Find the coordinates the point R shown.

 a. (- 3, 0, 0) b. (3, 0, 0) c. (0, 3, 0) d. (0, 0, 3)

#### Solution:

R is a point on the x - axis 3 units forward of origin O.
[Refer the figure.]

So, the coordinates of R are (3, 0, 0)
[Use positive sign for forwards.]

7.
Which of the following is correct?
 a. Trace of a plane is a circle b. Trace of a plane is a line segment c. Trace of a plane is a line d. Trace of a plane is a point

#### Solution:

A line that passes through two intercepts of a plane on the coordinate axes is called a trace of it.

So, trace of a plane is a line.

8.
Which of the following is correct?
 a. Every ordered pair of real numbers describes the position of a unique point of plane b. Every ordered triple of real numbers describes the position of a unique point of space c. Every ordered pair of real numbers describes the position of a unique point of space d. Both A and B

#### Solution:

To describe the position of a point of a plane two coordinates are needed and to describe the position of a point of space three coordinates are needed.

9.
If "7 units backward, 11 units right and 5 units down" describes the coordinates (- 7, 11, - 5) then the coordinates which describes "5 units forward, 7 units left and 10 units up" are
 a. (5, 7, - 10) b. (5, 7, 10) c. (5, - 7, 10) d. (- 5, 7, 10)

#### Solution:

It can be understood from the given description of the coordinates (- 7, 11, - 5) has, the positive sign for the coordinate stands for forward and negative stands for backward, the positive sign for the second coordinate stands for right and negative stands for left, the positive sign for the third coordinate stands for up and negative stands for down.

So, "5 units forward, 7 units left and 10 units up" can be described by the coordinates (5, - 7, 10).

10.
Which is the direction described by the point (0, - 2, 0) with respect to origin?
 a. Down b. Left c. Forward d. Up

#### Solution:

(0, - 2, 0) is the given point.

Since, x , y coordinates of the given point are zeros, it lies on the y - axis.

As, y - coordinate is - 2, the point describes left of origin.
[For y - coordinate, positive sign stands for right and negative sign stands for left.]