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11 a Plot the following points on a Cartesian plane and join the points in the order given, to draw the basic shape of a house.

(1, 5), (0, 5), (5, 10), (10, 5), (1, 5), (1, 0), (9, 0), (9, 5) b Describe a set of four points to draw a door. c Describe two sets of four points to draw two windows. d Describe a set of four points to draw a chimney. a Copy and complete the given table of values (all values are in centimetres). length (x) perimeter (y) 1 4 2 3 4 b Plot each pair of values to form a graph with length on the x-axis and perimeter on the y-axis. c Do these points lie in a straight line? a Decode Jake’s following message: (3, 2), (5, 1), (2, 3), (1, 4) b Code the word SECRET. c To increase the difficulty of the code, Jake does not include brackets or commas and he uses the origin to indicate the end of a word. d Code the phrase: BE HERE AT SEVEN.

12 The perimeter of a square is its length multiplied by 4. We can write this as a rule perimeter = 4 × length.

13 A grid system can be used to make secret messages. Jake decides to arrange the letters of the alphabet on a Cartesian plane in the following manner.

What do the following numbers mean?

13515500154341513400145354001423114354.

14 ABCD is a rectangle. The coordinates of A, B and C are given below. Draw each rectangle on a Cartesian plane and state the coordinates of the missing corner, D.

REASONING 15(1/2) 15 15, 16 a Find the coordinate of a possible third vertex. b Show on a Cartesian plane that there are infinite number of answers for this third vertex. c The area of the isosceles triangle is 10 square units. State the coordinates of the third vertex.

15 Write a rule (e.g. output = input × 2) that would give these graphs.

16 A(1, 0) and B(5, 0) are the base points of an isosceles triangle.

ENRICHMENT: Locating midpoints b Find the midpoint, M, of the line segment AB, which has coordinates A(2, 4) and B(0, 0). c Determine a method for locating the midpoint of a line segment without having to draw the points on a Cartesian plane. d Find the midpoint, M, of the line segment AB, which has coordinates A(6, 3) and B(2, 1) e Find the midpoint, M, of the line segment AB, which has coordinates A(1, 4) and B(4, 3) f Find the midpoint, M, of the line segment AB, which has coordinates A( 3, 2) and B(2, 3) g M(3, 4) is the midpoint of AB and the coordinates of A are (1, 5). What are the coordinates of B?

17 a Plot the points A(1, 4) and B(5, 0) on a Cartesian plane. Draw the line segment AB. Find the coordinates of M, the midpoint of AB, and mark it on the grid. (It needs to be halfway along the line segment.)