Bearings, Scale Drawing, Constructions & Loci Flashcards

All 29 cards in this deck

What are the three rules for writing a bearing?

Measured from north, clockwise, and written with three figures.
e.g. $25^\circ$ is written $025^\circ$

How do you find the back bearing (the bearing of A from B) when the bearing of B from A is less than $180^\circ$?

e.g. bearing of B from A is $147^\circ$

Add $180^\circ$.
$147 + 180 = 327^\circ$

How do you find the back bearing when the given bearing is more than $180^\circ$?

e.g. bearing of B from A is $250^\circ$

Subtract $180^\circ$.
$250 - 180 = 070^\circ$

True or false? The bearing of A from B is the same as the bearing of B from A.

False. They differ by $180^\circ$ (a back bearing).

Why are the north lines at two different points on a diagram useful when working out a bearing?

They are parallel, so alternate/co-interior angle facts link the two bearings.

What are the steps to mark a point from a given bearing and distance?

e.g. R is 55 km from T on a bearing of $065^\circ$, scale 1 cm to 10 km

1. Convert the distance with the scale: $55 \div 10 = 5.5$ cm
2. Draw a north line at T and measure $065^\circ$ clockwise from it
3. Measure 5.5 cm along that direction and mark R with a cross

On a map, what does a scale of $1:25\,000$ mean?

1 unit on the map represents $25\,000$ of the same unit in real life.

How do you convert a map length into a real distance?

e.g. 8 cm on a map with scale 1 cm to 4 km

Multiply the map length by the scale.
$8 \times 4 = 32$ km

How do you find the length to draw on a map for a given real distance?

e.g. real length 10 km, scale 1 cm to 4 km

Divide the real distance by the scale.
$10 \div 4 = 2.5$ cm

To change a real distance in cm into km, what do you divide by?

$100\,000$.
e.g. $350\,000$ cm $\div\ 100\,000 = 3.5$ km

True or false? A scale of $1:1200$ means 1 cm on the drawing represents 1200 cm in real life.

True. $1200$ cm is 12 m, so 1 cm represents 12 m.

What are the steps to estimate a real height from a picture using a known reference length?

e.g. a bus of real length 12 m measures 2 cm; the building measures 5 cm

1. Measure both the reference object and the unknown object on the picture: 2 cm and 5 cm
2. Find the scale factor between them: $5 \div 2 = 2.5$
3. Multiply the known real length by it: $12 \times 2.5 = 30$ m

What are the steps to make a scale drawing of a rectangle?

e.g. a 35 m by 20 m rectangle, scale 1 cm to 5 m

1. Divide each real length by the scale: $35 \div 5 = 7$, $20 \div 5 = 4$
2. Draw accurately with a ruler: a 7 cm by 4 cm rectangle
3. Measure the drawing and convert back to find any real measurement

Which instrument do you need to construct a triangle given three sides (SSS)?

Ruler and compasses (no protractor needed).

What are the steps to construct a triangle given three sides (SSS)?

e.g. sides 8 cm, 6 cm, 6 cm

1. Draw the longest side with a ruler: 8 cm
2. Set compasses to 6 cm, arc from one end
3. Set compasses to 6 cm, arc from the other end; join the crossing point to both ends

What are the steps to construct a triangle given two sides and the angle between them (SAS)?

e.g. sides 7 cm and 5 cm with a $40^\circ$ angle between them

1. Draw one side: 7 cm
2. Measure the angle at one end with a protractor: $40^\circ$
3. Measure the second side along that arm (5 cm) and join to complete the triangle

What are the steps to construct a triangle given two angles and the side between them (ASA)?

e.g. a 6 cm side with angles $50^\circ$ and $70^\circ$ at its ends

1. Draw the given side: 6 cm
2. Measure $50^\circ$ at one end and draw a long line
3. Measure $70^\circ$ at the other end and draw a line; they meet at the third vertex

True or false? When constructing a triangle you should rub out the compass arcs to make the drawing neat.

False. Construction arcs must be left visible or marks are lost.

What tolerance is normally allowed for accurate constructions and measurements?

Lengths within about $\pm 2$ mm and angles within about $\pm 2^\circ$.

What two properties does the perpendicular bisector of AB have?

It crosses AB at $90^\circ$ through its midpoint, and every point on it is equidistant from A and B.

What is true of every point on the bisector of an angle?

It is equidistant from the two arms (lines) of the angle.

What is the shortest distance from a point to a line?

The perpendicular distance from the point to the line.

What is a locus?

The set of all points that satisfy a given rule or condition.

What is the locus of points a fixed distance from a single point?

A circle, centre that point, with radius equal to that distance.

What is the locus of points a fixed distance from a straight line segment?

Two parallel lines, one each side at that distance, joined by semicircles at the ends.

Which construction gives the locus of points equidistant from two points A and B?

The perpendicular bisector of AB.

Which construction gives the locus of points equidistant from two lines that meet?

The bisector of the angle between them.

What are the steps to shade a region satisfying two loci conditions?

e.g. inside a triangle, less than 4 cm from A and closer to C than to B

1. Draw the first locus: an arc of radius 4 cm, centre A
2. Draw the second locus: the perpendicular bisector of CB
3. Shade only the overlap: inside the arc and on C's side of the bisector

True or false? On a scale plan with scale $1:30$, "more than 180 cm from A" is drawn as an arc of radius 180 cm.

False. Convert first: $180 \div 30 = 6$ cm, so draw an arc of radius 6 cm and shade outside it.