Great Lakes College Tuncurry Junior Campus

Great Lakes College ~ Tuncurry Junior Campus Year 10 Mathematics Topic Test Coordinate Geometry

Name: ______Instructions 1. Answer all questions. 2. Show all necessary working. 3. Multiple-choice questions circle the most correct answer.

Section One 15 multiple-choice questions 2 marks each Question One The value of the triangle in 2 122 13 could be

A. 1 B. -1 C. -13 D. 5

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

A. y  1 B. y  x  1 C. y  x 1 D. y  x  1

Question Four The graph of x  0

A. has zero gradient B. is the x-axis C. is the y axis D. has no y-intercept

Question Five the y-intercept of y  3x  6 is

A.  6 B. 2 C. 3 D.  3

1 Question Six Which of these lines is not parallel to the other three?

A. y  4  x B. y  6  4x C. y  4x D. y  4x  10

Question Seven From the diagram below, the coordinates of the midpoint of AB are

y 4 A3,4

-4 -3 -2 -1 0 1 2 3 4 x

-1

-2 B-3,-2

 1 1   1 1  A.  ,  B.  ,  C. 1,0 D. 0,1 2 2  2 2

Question Eight The length of the interval AB in the diagram below is

A 2,1 1

-3 -2 -1 1 2 3 -1

-2 B -2,-2

A. 4 B. 5 C. 6 D. 3

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

-2 -1 0 1 x -1

A. 0 B. -2 C. 3 D. unknown

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?

A. y  4x B. y  1 C. x  4 D. y  x  4

3 Question Fourteen Which of these points lies on the line y  3x  3 ?

A. ( 2, 2 ) B. ( -1, 1 ) C. ( 3,12 ) D. ( 2,6 )

Question Fifteen 3y  3x  3 can be rewritten as:

A. y  x  1 B. y  x  1 C. y  3x  1 D. y  3x  3

Section Two Question One Complete the table of values for y  3x  4

X -3 -2 -1 0 1 2 3 Y

Question Two 2 marks Write any equation of a straight line that has a y – intercept of 4 ______

Question Three 2 marks

Draw the graph of x  3 on a the number plane

y 3

-3 -2 -1 0 1 2 3 x -1

-2

-3

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 ______

5 Question Six 4 marks Find the equation of this line

-5 -2 -1 0 1 x

______

6 REVISION NOTES for COORDINATE GEOMETRY

1. Application of Pythagoras theorem 2  2  2 c a b c or c  a 2  b 2 b

2. Slope of straight lines that have a. + positive gradient eg +4 b. – negative gradient eg -2

3. Interpretation of y  mx  b where m is the gradient value and b is the y – intercept

4. Given the gradient and y – intercept give the equation of the straight line.

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

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.

7. Identify the value that parallel lines share. The same gradient value

8. The equations of the axises on a number plane

9. Given the coordinates of a point determine whether this point is on a given line.