Revision Coordinate Geometry. Question 1: The gradient of the line joining the points V (k, 8) and W (2, k +1) is is.
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1 Question 1: 2 The gradient of the line joining the points V (k, 8) and W (2, k +1) is is. 3 a) Find the value of k. b) Find the length of VW.
2 Question 2: A straight line passes through A( 2, 3) and B( 2, 6). Find a) the length of AB. b) the gradient of AB. c) the equation of line AB. d) coordinates of the point at which the line AB intersects the x-axis.
3 Question 3: Given points A and B have coordinates (3, 1) and (-5, 7), find the a) equation of AB. b) value of k if the point (2k, -2) lies on the line AB. c) length of AB. d) value of a if the line 4y = 3ax + 4 is parallel to the AB.
4 Question 4: a) Given that A is the point (5, 8) and B is the point (3, 2), i. find the gradient of the line AB, ii. find the equation of the line AB. Another line CD passes through (0, 5) and has the same gradient as AB. b) State the equation of line CD. c) Calculate the value of h if ( h, 1) lies on line CD.
5 Question 5: The diagram shows a sketch of the graph of 2y = a 3x. The line crosses the axes at A and B. (0,6) B y a) Write down the gradient of the line AB. b) Given that the y-intercept is 3, find the value of a. c) Calculate the length of the line joining A and B. O (2,0) A x 2y a 3x
6 Question 6: CD is a straight line, as shown in the diagram. The line CD cuts the y-axis at (0, 3). a) Calculate the gradient of the line CD. b) Hence find the value of k. c) Find the equation of a line which passes through C, with a gradient of 3. d) Point E is positioned such that triangle CED is a right angled triangle. Write down two possible coordinates of point E.
7 Question 7: In the diagram, OPQR is a trapezium where O is the origin, and PQ is parallel to OR. The coordinates of P is (-5, 9). a) State the coordinates of Q. b) Write down the equation of line PQ. c) Find the equation of the line OP. d) Given that the area of the trapezium OPQR is 72 units 2, find the coordinates of R. y P( 5, 9) Q O R x
8 Question 8: The points A (-5, 5), B (1, -3) and C (4, -3) are shown in the diagram. Find a) the gradient of line AB. y b) the equation of the line AB. c) the length of AB. d) the area of triangle ABC. A (-5, 5) x B (1, -3) C (4, -3)
9 Question 9: In the given diagram, the equation of line l is 2y = 4x + 5 and the point S(a, 2) lies on the line l. It is given that line l intersects the x-axis and y-axis at B and A respectively. a) Find the gradient of line l. y b) Find the value of a. c) Find the coordinates of A and B. S A line l B O x
10 Question 10: In the diagram, B is the point (0, 16) and C is the point (0, 6). The sloping line through B and the horizontal line through C meet at the point A. a) Write down the equation of the line AC. b) Given that the gradient of the line AB is 2, find the equation of the line AB. c) Calculate the coordinates of the point A. d) Calculate the area of the ABC.
11 Question 11: A straight line l1 passes through the point (1, 10) and (3, 14). a) Find the equation of line. b) A straight line is parallel to l and passes through the point ( 3, 7). Find the equation of line. l 1 l 2 1 l 2
12 Question 12: Find the equation of the line which is parallel to the line x + 3y + 6 = 0 and passes through the point ( 4, 2).
13 Question 13: The diagram shows a triangle ABC with points A(1, 4), B(8, 4) and C(10, 9). a) Find the gradient of AC. b) Given that a line parallel to AC passes through a point (0, 6), y find the equation of this line. c) Calculate the area of triangle ABC. C(10, 9) A(1, 4) B(8, 4) x
14 Question 14: The diagram shows a triangle with coordinates A( 2, 1), B(6, 1) and C(3, 4). Find a) the equation of BC, y b) the area of ABC, C 4 c) the area of AXB, given that X is a point on AC such that AX : XC = 3 : 2. A B x
15 Question 15: The graphs of 2 linear equations are shown below. It is given that the coordinates of Q are (0, 8), the coordinates of R are (6, 0) and the area of is 32 cm 2. The equation of line PQ is y = ax + b. Find a) the coordinates of P, b) the values of a and b.
16 Question 16: ABCD is a trapezium in which BC is 5 units. If A is the point (-3, 0), B is the point (-1, 4) and the area of the trapezium is 30 square units, find the a) coordinates of the point C, b) coordinates of the point D, c) the equation of CD.
17 Question 17: In the diagram, the equation of the line AC is 3y 2x 30 = 0. The length of the line BC is 10 units. a) Find the coordinates of C. b) State the coordinates of B. c) Find the area of triangle ABC. d) Find the length of the perpendicular from B to AC.
18 Revision Accomplished!
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