Page 83 - Mathematics Class - XII

TOPIC - 7: Three-Dimensional Geometry

ACTIVITY 7.1

OBJECTIVE
To locate the points to given coordinates in space, measure the distance between two points in space and then to
verify the distance using distance formula.

MATERIAL REQUIRED
Y Cardboard/drawing board Y Eraser

Y Graph paper Y Wires
Y Adhesive Y Tooth picks of different length

Y Pens Y Paper arrow heads
Y Geometry box

PRE-REQUISITE KNOWLEDGE
1. Knowledge of the concept of coordinate geometry.
2. Knowledge of the concept of distance formula in 3-dimensional geometry.

PROCEDURE

1. Take a drawing board/cardboard and paste a graph paper on it.
2. Draw two lines X'OX and Y'OY to represent x-axis, y-axis respectively (see Fig. (a)) and take 1 unit = 1 cm.

3. Fix a wire through O, in the vertical direction, representing the z-axis.
4. Plot the points P (4, 5), Q (–3, 3), R (5, –1), S (–5, –6), T (4, 0) and U (0, –5) on the graph paper.
5. Fix toothpicks of length 1 cm, 2 cm, 3 cm, 4 cm, 5 cm, 6 cm vertically at points P (4, 5), Q ( –3, 3),
R (5, –1), S (–5, –6), T (4, 0) and U (0, –5) on the graph paper. Now the upper tips of these toothpicks
represent the points A, B, C, D, E and F respectively in the space.

DEMONSTRATION
1. Coordinates of the point A = (4, 5, 1).

2. Coordinates of the point B = (–3, 3, 2).
3. Similarly find the coordinates of the points C and D.

4. Using a scale: the distance AB = 7.3 cm.

5. Using distance formula; AB = ( 34 ) ( 35 ) ( 21 ) 49 41 . 735 cm
2
2
2
Thus, the distance AB, obtained by actual measurement is approximately same as the distance obtained by
using the distance formula.
Same can be verified for other pairs of points (A, C); (B, C); (A, D); (C, D); (B, D).

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