math l2 module 8

Mathematics NQF Level 2 Downloaded from hlayiso.com *see terms and conditions Mathematics NQF Level 2

Using the Cartesian coordinate system to derive and apply equations Module 8 Downloaded from hlayiso.com Mathematics NQF Level 2

Learning activity 8.1 Downloaded from hlayiso.com Mathematics NQF Level 2

4. Video − Draw a polygon by plo ng the ver ces given as A(−1; −2), B(1; −2), C(−2; 0), D(2; 0), E(−1; 2) and F(1; 2). Click above to play this video. Downloaded from hlayiso.com Learning activity 8.1

Calculating the distance between two points in the Cartesian plane AB2  x 2  y 2  ( x2  x1 ) 2  ( y2  y1 ) 2  AB  ( x2  x1 ) 2  ( y2  y1 ) 2 Figure 8.8: Distance formula Downloaded from hlayiso.com Unit 8.2

The gradient of a line joining two points y y2  y1 Gradient m   x x2  x1 Downloaded from hlayiso.com Unit 8.3

Learning activity 8.4 Downloaded from hlayiso.com Mathematics NQF Level 2

5. Calculate x1 and y1 if M(3; −2) is the midpoint of the line segment joining P(2; −4) and Q(x1; y1) . P(2;  4) and Q and M(3;  2) ( x2 ; y 2 ) ( x1 ; y1 ) ( x; y ) Downloaded from hlayiso.com Learning activity 8.4

5. (continued) P(2;  4) and Q and M(3;  2) ( x2 ; y 2 ) ( x1 ; y1 ) ( x; y ) x1  x2 x 2 x1  2 3 2 6  x1  2 4  x1  x1  4 ( x1; y1 )  (4; ) Downloaded from hlayiso.com Learning activity 8.4

5. (continued) P(2;  4) and Q and M(3;  2) ( x2 ; y 2 ) ( x1 ; y1 ) ( x; y ) y1  y2 y 2 y1  (4) 2  2 4  y1  4 0  y1  y1  0 ( x1; y1 )  (4;0) Downloaded from hlayiso.com Learning activity 8.4

Summative assessment Module 8 Downloaded from hlayiso.com Mathematics NQF Level 2

1. Calculate x1 and y1 if M(−2; 4) is the midpoint of the line segment joining P(−1; −1) and Q (x1; y1). P(  1;  1) and Q and M(  2; 4) ( x2 ; y 2 ) ( x1 ; y1 ) ( x; y ) Downloaded from hlayiso.com Summative assessment – Module 8

1. (continued) P(  1;  1) and Q and M(  2; 4) ( x2 ; y 2 ) ( x1 ; y1 ) ( x; y ) x1  x2 x 2 x1  1 2  2 4  x1  1  x1  3 ( x1; y1 )  (3; ) Downloaded from hlayiso.com Summative assessment – Module 8

1. (continued) P(  1;  1) and Q and M(  2; 4) ( x2 ; y 2 ) ( x1 ; y1 ) ( x; y ) y1  y2 y 2 y1  (1) 4 2 8  y1  1  y1  9 ( x1; y1 )  (3;9) Downloaded from hlayiso.com Summative assessment – Module 8

2. Calculate the length of the line that joins point A(1; 2) to the midpoint of the line joining P(−2; 3) and Q(2; −3). A(1; 2) and P(  2; 3) and Q(2;  3) ( x1 ; y1 ) ( x2 ; y 2 ) Midpoint of PQ = M( x; y ) Downloaded from hlayiso.com Summative assessment – Module 8

2. (continued) x1  x2 y1  y2 x y 2 2 2  2 3  (3) x y 2 2 x  0 y 0 Midpoint of PQ: M( x; y )  M(0;0) Downloaded from hlayiso.com Summative assessment – Module 8

2. (continued) M(0;0) and A(1;2) ( x1 ; y1 ) ( x2 ; y 2 ) MA  ( x2  x1 ) 2  ( y2  y1 ) 2  (1  0) 2  (2  0) 2  4 1  5  2, 236 units Downloaded from hlayiso.com Summative assessment – Module 8

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 8

4. Plot the points A(−2; 0) and B(3; 3) on a set of coordinate axes. A   2; 0  and B  3; 3  ( x1 ; y1 ) ( x2 ; y 2 ) Downloaded from hlayiso.com Summative assessment – Module 8

4. Plot the points A(−2; 0) and B(3; 3) on a set of coordinate axes. 4.1 Calculate the gradient of AB. y y2  y1 Gradient m   x x2  x1 30  3  (2) 3  5 hlayiso.com Downloaded from Summative assessment – Module 8

4. Plot the points A(−2; 0) and B(3; 3) on a set of coordinate axes. 4.2 Calculate the length of AB. 2 2 Length of AB  ( x2  x1 )  ( y2  y1 ) 2 2  (3  (2))  (3  0)  25  9  5,83 units Downloaded from hlayiso.com Summative assessment – Module 8

4. Plot the points A(−2; 0) and B(3; 3) on a set of coordinate axes. 4.3 Calculate the midpoint of line AB. x1  x2 y1  y2 x y 2 2 3  (2) 3 0 x y 2 2 1 3   2 2 1 3 Midpoint  ( ; ) Downloaded2 from 2 hlayiso.com Summative assessment – Module 8

Downloaded from hlayiso.com Mathematics NQF Level 2