Graphs Topical question[CIE Extended Mathematics (0580) (2017-2018)]

Regarding Graphs

Do you know

• Gradient of a straight line, 
• The equation of a straight line, 
• Distance between the two points, 
• Midpoint of a line segment, 
• Parallel and perpendicular lines, 
• Interpracting graph, 
• y intercept, x intercept. 

If YES ---> you can practice topic questions.

1	(2017/s/21/q12) A line has gradient \(5\).  \(M\) and \(N\) are two points on this line. \(M\) is the point \((x, 8)\) and \(N\) is the point \((k, 23)\).  Find an expression for \(x\) in terms of \(k\).[3]
2	(2017/w/21/q6) The diagram shows two sides of a rhombus \(ABCD\). (a) Write down the co-ordinates of \(A\).[1] (b) Complete the rhombus \(ABCD\) on the grid.[1]
3	(2018/s/21/q24) (a) Point \(A\) has co-ordinates \((1, 0)\) and point \(B\) has co-ordinates \((2, 5)\).  Calculate the angle between the line \(AB\) and the \(x\)-axis.[3]  (b) The line \(PQ\) has equation \(y = 3x - 8\) and point \(P\) has co-ordinates \((6, 10)\). Find the equation of the line that passes through \(P\) and is perpendicular to \(PQ\). Give your answer in the form \(y = mx + c\).[3]
4	(2017/m/22/q20) (a) Find the equation of the line \(l\).  Give your answer in the form \(y = mx + c\).[3]  (b) A line perpendicular to the line \(l\) passes through the point \((3, -1)\). Find the equation of this line.[3]
5	(2017/s/22/q27) \(A\) is the point \((-2, 0)\) and \(B\) is the point \((0, 4)\).  (a) Find the equation of the straight line joining \(A\) and \(B\).[3] (b) Find the equation of the perpendicular bisector of \(AB\).[4]
6	(2018/s/22/q25) (P\) is the point \((16, 9)\) and \(Q\) is the point \((22, 24)\).  (a) Find the equation of the line perpendicular to \(PQ\) that passes through the point \((5, 1)\).  Give your answer in the form \(y = mx + c\).[4]  (b) \(N\) is the point on \(PQ\) such that \(PN = 2NQ\).  Find the co-ordinates of \(N\).[2]
7	(2018/w/22/q10) Find the mid-point of \(AB\) where \(A = (w, r)\) and \(B = (3w, t)\).  Give your answer in its simplest form in terms of \(w, r\) and \(t\). [2]
8	(2018/w/22/q17) The diagram shows the points \(C(-1, 2)\) and \(D(9, 7)\).  Find the equation of the line perpendicular to \(CD\) that passes through the point \((1, 3)\). Give your answer in the form \(y = mx + c\).[4]
9	(2017/s/41/q7) A line joins the points \(A(-3, 8)\) and \(B(2, -2)\).  (a) Find the co-ordinates of the midpoint of \(AB\).[2] (b) Find the equation of the line through \(A\) and \(B\). Give your answer in the form \(y = mx + c\).[3] (c) Another line is parallel to \(AB\) and passes through the point \((0, 7)\).  Write down the equation of this line.[2] (d) Find the equation of the line perpendicular to \(AB\) which passes through the point \((1, 5)\).  Give your answer in the form \(ax + by + c = 0\) where \(a, b\) and \(c\) are integers.[4]
	to be continued....

Answer Key

1. \( k-3 \)

2. (a) \( (-2,3) \) (b)Correct rhombus with 4 th point at \( (2,2) \);

3. (a) 78.7 (b) \( y=-\frac{1}{3} x+12 \)

4. (a) \( [y=]-2 x+3 \) (b) \( y=\frac{1}{2} x-\frac{5}{2} \)

5. (a) \( y=2 x+4 \) (b) \( y=-\frac{1}{2} x+\frac{3}{2} \)

6. (a) \( [y=]-\frac{2}{5} x+3 \) (b) \( (20,19) \)

7. \( \left(2 w, \frac{r+t}{2}\right) \)

8. \( -2 x+5 \)

9. (a) \( (-0.5,3) \) (b) \( [y=]-2 x+2 \) (c) \( y=-2 x+7 \) (d) \( x-2 y+9=0 \) or \( 2 y-x-9=0 \)

10. (a) \( (5,6) \) (b) \( [y=] \frac{v^{4}}{5} x+3 \) (c) \( [y=] \frac{4}{5} x- \) 2 (d) (i) \( [y=] \frac{5}{4} x+4 \) (d) (ii) 8.54 or 8.544 (d) (iii) \( (4,6) \)

11. (a) 10.8 or 10.81 to 10.82 (b)(i) (6, 4) (ii) 2

(iii) \( y=-\frac{1}{2} x+4 \)