Year 8AC9M8SP03

Position in Three Dimensions

Describe the position and location of objects in 3 dimensions in different ways, including using a three-dimensional coordinate system. Design, create and test algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describe how the algorithm works.

Two numbers fix a point on a page. Three fix a point in a room. The third coordinate is just height, and it works exactly like the other two.

Method

Three coordinates

(x, y, z)

Across, along, then up.

Order never changes

The same rule as 2D, with one more number on the end.

Zero means on that plane

(3, 4, 0)

This point sits flat on the floor.

An algorithm is fixed questions in a fixed order

Same questions, same order, same answer every time.

Worked example

e.g.

\text{Describe the point } (2, 5, 3) \text{ in a room.}

Start at the corner of the room, the origin. $(0,0,0)$
The first number is across. $2 \text{ metres along one wall}$
The second is along the other direction. $5 \text{ metres out from that wall}$
The third is up. $3 \text{ metres above the floor}$
State it in plain words. $\text{2 across, 5 along, 3 up}$

Practice

Across, along, up. Always in that order.

\text{Where is } (0,0,4)?

Answer

\text{Directly above the origin, 4 up.}

\text{A point has } z = 0. \text{ Where is it?}

Answer

\text{On the floor.}

\text{Is } (1,2,3) \text{ the same as } (3,2,1)?

Answer

\text{No. The order matters.}

\text{Write an algorithm to test if two triangles are congruent.}

Answer

\text{Compare 3 sides. If equal, SSS. If not, compare 2 sides and the included angle, and so on.}

\text{Why must the algorithm ask in a fixed order?}

Answer

\text{So the same pair always gives the same answer.}

\text{How many numbers fix a point on a page?}

Answer

\text{Two.}