<p> Great Lakes College ~ Tuncurry Junior Campus Year 10 Mathematics Topic Test Coordinate Geometry </p><p>Name: ______Instructions 1. Answer all questions. 2. Show all necessary working. 3. Multiple-choice questions circle the most correct answer.</p><p>Section One 15 multiple-choice questions 2 marks each Question One The value of the triangle in 2 122 13 could be </p><p>A. 1 B. -1 C. -13 D. 5</p><p>Question Two 1 The gradient of y  4x  is 2 1 1 A. B. 4 C.  4 D.  2 2 Question Three Which of these lines has a gradient of  1</p><p>A. y  1 B. y  x  1 C. y  x 1 D. y  x  1 </p><p>Question Four The graph of x  0 </p><p>A. has zero gradient B. is the x-axis C. is the y axis D. has no y-intercept</p><p>Question Five the y-intercept of y  3x  6 is</p><p>A.  6 B. 2 C. 3 D.  3 </p><p>1 Question Six Which of these lines is not parallel to the other three?</p><p>A. y  4  x B. y  6  4x C. y  4x D. y  4x  10 </p><p>Question Seven From the diagram below, the coordinates of the midpoint of AB are</p><p> y 4 A3,4</p><p>3</p><p>2</p><p>1</p><p>-4 -3 -2 -1 0 1 2 3 4 x</p><p>-1</p><p>-2 B-3,-2</p><p> 1 1   1 1  A.  ,  B.  ,  C. 1,0 D. 0,1 2 2  2 2</p><p>Question Eight The length of the interval AB in the diagram below is </p><p>2</p><p>A 2,1 1</p><p>-3 -2 -1 1 2 3 -1</p><p>-2 B -2,-2</p><p>A. 4 B. 5 C. 6 D. 3</p><p>2 Question Nine Using the diagram in Question Eight the gradient of AB is ( the formula is Rise Gradient  ) Run 4 3 A. -1 B. C. D. 1 3 4 Question Ten Using the diagram below the y - intercept is y 4</p><p>3</p><p>2</p><p>1</p><p>-2 -1 0 1 x -1</p><p>A. 0 B. -2 C. 3 D. unknown</p><p>Question Eleven Using the diagram in Question Ten the gradient of the line is 2 2 3 3 A.  B. C. D.  3 3 2 2 Question Twelve Combining the answers of Question Ten and Question Eleven, the equation for the line in Question Ten is 3 3 2 2 A. y  x  3 B. y   x  2 C. y   x D. y  x  3 2 2 3 3 Question Thirteen Which line is parallel to y  4?</p><p>A. y  4x B. y  1 C. x  4 D. y  x  4 </p><p>3 Question Fourteen Which of these points lies on the line y  3x  3 ?</p><p>A. ( 2, 2 ) B. ( -1, 1 ) C. ( 3,12 ) D. ( 2,6 )</p><p>Question Fifteen 3y  3x  3 can be rewritten as:</p><p>A. y  x  1 B. y  x  1 C. y  3x  1 D. y  3x  3</p><p>Section Two Question One Complete the table of values for y  3x  4 </p><p>X -3 -2 -1 0 1 2 3 Y</p><p>Question Two 2 marks Write any equation of a straight line that has a y – intercept of 4 ______</p><p>Question Three 2 marks</p><p>Draw the graph of x  3 on a the number plane </p><p> y 3</p><p>2</p><p>1</p><p>-3 -2 -1 0 1 2 3 x -1</p><p>-2</p><p>-3</p><p>4 Question Four 2 marks Write the equation of a line that has a gradient of 7 and a y – intercept of -3 ______Question Five The straight line AB on a number plane has the endpoints A ( -3,1 ) and B ( 7,5 ) Find: a. the gradient of AB 2 marks ______b. the length of AB as a surd ( exact value ) 2 marks ______c. the midpoint of AB 2 marks ______</p><p>5 Question Six 4 marks Find the equation of this line</p><p> y</p><p>8</p><p>6</p><p>4</p><p>2</p><p>-5 -2 -1 0 1 x</p><p>______</p><p>6 REVISION NOTES for COORDINATE GEOMETRY</p><p>1. Application of Pythagoras theorem 2  2  2 c a b c or c  a 2  b 2 b</p><p> a</p><p>2. Slope of straight lines that have a. + positive gradient eg +4 b. – negative gradient eg -2</p><p>3. Interpretation of y  mx  b where m is the gradient value and b is the y – intercept </p><p>4. Given the gradient and y – intercept give the equation of the straight line.</p><p>5. From a sketch of a straight line on a number plane identify the y – intercept Rise and be able to calculate the gradient using m  . Run</p><p>6. Given the endpoints of a straight line be able to calculate the a. the midpoint. b. the length of the line. c. the gradient of the line. using the appropriate formulae for each. </p><p>7. Identify the value that parallel lines share. The same gradient value</p><p>8. The equations of the axises on a number plane</p><p>9. Given the coordinates of a point determine whether this point is on a given line. </p><p>7</p><p>8</p>