Page 123 - Cambridge+Checkpoint+Mathematics+Coursebook+9

12.5 Drawing a locus

6 Draw the capital letters T, L and C on centimetre-squared paper.
For each letter, draw the locus of points that are 1 cm from the letter.
a b c

W X

7 The diagram shows a rectangular field WXYZ.
There is a fence around the perimeter of the field.
Gary the goat is tied by a rope to corner X of the field.
When the rope is tight, Gary can just reach corner Y.
Copy the diagram on plain paper.
a Draw the locus of points that Gary can reach when
the rope is tight. Z Y
b Shade the region inside which Gary can move.
P Q
8 The diagram shows two schools, P and Q, 70 km apart. 70 km
Students can go to a school if they live less than 40 km from that school.
Copy the diagram on plain paper. Use a scale of 1 cm to 5 km.
a Draw the locus of points that are exactly 40 km from P.
b Draw the locus of points that are exactly 40 km from Q.
c Tanesha can go to either school. Shade the region in which Tanesha must live.

Summary

You should now know that: You should be able to:
+ A tessellation is a repeating pattern made by + Tessellate triangles and quadrilaterals and relate
fitting together copies of a given shape, without to angle sums and half-turn rotations; know which
any gaps or overlaps. You can move the original regular polygons tessellate and explain why
shape by translating, rotating or reflecting it. others will not.
+ Many tessellations can be made by using the + Use a coordinate grid to solve problems
shape itself and a half-turn rotation of the shape. involving translations, rotations, reflections and
+ In any tessellation, the sum of the angles where enlargements.
vertices of shapes meet is 360°. + Transform 2D shapes by combinations of rotations,
+ A column vector describes a translation of a shape reflections and translations; describe the
on a coordinate grid. The top number describes transformation that maps an object to its image.
a move to the right or left. The bottom number + Enlarge 2D shapes, given a centre and scale
describes a move up or down. factor; identify the scale factor of an enlargement.
+ To describe a reflection, you state the equation of + Recognise that translations, rotations and
the mirror line. reflections preserve length and angle, and
+ To describe a translation you can use a column vector. map objects onto congruent images, and that
enlargements preserve angle but not length.
+ To describe a rotation, you state the centre of
rotation, the number of degrees of the rotation + Know what is needed to give a precise
and the direction of the rotation. description of a reflection, rotation, translation or
enlargement.
+ When you describe an enlargement you must
state the scale factor of the enlargement and the + Find, by reasoning, the locus of a point that moves
position of the centre of enlargement. at a given distance from a fixed point, or at a given
distance from a fixed straight line.
+ A locus is a set of points that follow a given rule.

122 12 Tessellations, transformations and loci