Grade 11- Mathematics Question Paper and Memo by Maths Wizard

Question 1 (20 minutes) (a) On the diagram below, represent the point . (2)(b) Now represent the following points on the diagram provided on the previous page: Point B, the rotation of point A, anticlockwise about the origin. Point C, the rotation of point A, about the origin. Point D, the rotation of point A, clockwise about the origin. (3) (c) Write down algebraic rules to describe the above transformations. (3) (d) What type of quadrilateral is figure ABCD? Explain by referring to the properties of quadrilaterals. (2) (e) Figure ABCD is enlarged by a scale factor of 2 units through the origin to form its image ////. On the diagram provided on the previous page, sketch the image ////A B C D and indicate the coordinates of the vertices. (2) (f) Determine the ratio: ////Area ABCD Area A B C D (1) (g) ABCD is reflected about the y-axis to form its image EFGH. (1) Write down the coordinates of E. (1) (2) Determine the ratio: (1) (h) Describe, using words and algebraic notation, the single transformations involved if figure ABCD is transformed by the rule: 1 1 ( ; ) ; 1 2 2 x y x y (3)Question 1 (a), (b) (b) B( 2; 3) C(3; 2) D(2;3) D(2;3) (3) (c) 90 anticlockwise: anti-clockwise or clockwise: 90 clockwise: (3) (d) ABCD is a square since: Diagonals are equal in length Diagonals bisect each other at right angles square properties (2)(e) ////A ( 6; 4) B ( 4; 6) C (6; 4) D (4;6) See diagram correct coordinates indicated joining points to form enlarged square (2) (f) ////2 Area ABCD 1 14 Area A B C D 2 (1) (g)(1) E(3;2) answer (1) (g)(2) Perimeter ABCD 4 side AB 1 Perimeter EFGH 4 side EF (since AB EF) answer (1) (h) 1 1 1 ( ; ) ; reduction by a factor of 2 2 2 1 1 1 1 ; ; reflection about axis 2 2 2 2 1 1 1 1 ; ; 1 translation of 1 unit downwards 2 2 2 2 1 1 ( ; ) ; 1 2 2 x y x y x y x y x x y x y x y x y reduction reflection translation (3) See Section C (Enlargement and reduction rules)