(a) Using a scale of 2cm to 2units on both axes, draw on a sheet of graph paper two perpendicular axes 0x and 0y for \(-10 \leq x \leq 10\) and \(-10 \leq y...
Assessment:WAEC SSCE - General Mathematics - 2018Subject:General Mathematics
(a) Using a scale of 2cm to 2units on both axes, draw on a sheet of graph paper two perpendicular axes 0x and 0y for \(-10 \leq x \leq 10\) and \(-10 \leq y \leq 10\)
(b) Given the points P(3, 2). Q(-1. 5). R(0. 8) and S(3, 7). draw on the same graph, indicating clearly the vertices and their coordinates, the:
(i) quadrilateral PQRS;
(ii) image \(P_1Q_1R_1S_1\) of PQRS under an anticlockwise rotation of \(90^o\) about the origin where \(P \to P_1\), \(Q \to Q_1\), \(R \to R_1\) and \(S \to S_1\)
(iii) image \(P_2Q_2R_2S_2\) of \(P_1Q_1R_1S_1\) under a reflection in the line \(y - x = 0\) where \(P_1 \to P_2\), \(Q_1 \to Q_2\), \(R_1 \to R_2\) and \(S_1 \to S_2\)
(c) Describe precisely the single transformation T for which \(T : PQRS \to P_2Q_2R_2S_2\)
(d) The side \(P_1Q_1\) of the quadrilateral \(P_1Q_1R_1S_1\) cuts the x-axis at the point W. What type of quadrilateral is \(P_1S_1R_1W\)?
(a) and (b) The required coordinate graph, drawn to equal scales on both axes, is shown below. The vertices are joined in the order in which they are named.
Coordinate graph showing the original quadrilateral, its 90° anticlockwise rotation about the origin, and the reflection of that image in the line y = x.
The coordinates plotted are:
Object
Vertices
PQRS
P(3,2), Q(-1,5), R(0,8), S(3,7)
P1Q1R1S1
P1(-2,3), Q1(-5,-1), R1(-8,0), S1(-7,3)
P2Q2R2S2
P2(3,-2), Q2(-1,-5), R2(0,-8), S2(3,-7)
For a rotation of \(90^\circ\) anticlockwise about the origin, \((x,y)\mapsto(-y,x)\). Thus, for example, \(P(3,2)\mapsto P_1(-2,3)\).
Reflection in \(y=x\) maps \((x,y)\mapsto(y,x)\). Thus \(P_1(-2,3)\mapsto P_2(3,-2)\).
(a) and (b) The required coordinate graph, drawn to equal scales on both axes, is shown below. The vertices are joined in the order in which they are named.
Coordinate graph showing the original quadrilateral, its 90° anticlockwise rotation about the origin, and the reflection of that image in the line y = x.
The coordinates plotted are:
Object
Vertices
PQRS
P(3,2), Q(-1,5), R(0,8), S(3,7)
P1Q1R1S1
P1(-2,3), Q1(-5,-1), R1(-8,0), S1(-7,3)
P2Q2R2S2
P2(3,-2), Q2(-1,-5), R2(0,-8), S2(3,-7)
For a rotation of \(90^\circ\) anticlockwise about the origin, \((x,y)\mapsto(-y,x)\). Thus, for example, \(P(3,2)\mapsto P_1(-2,3)\).
Reflection in \(y=x\) maps \((x,y)\mapsto(y,x)\). Thus \(P_1(-2,3)\mapsto P_2(3,-2)\).
