8/18/2019 Coordinate Geometry Revision

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Preliminary Mathematics Assessment Task 29-7-05

STRAIGHT LINE GRAPHS 

7. P ( - 3 , 2 ) , Q ( 2 , 1 ) and R (-1 , -2) are three points on the number plane. 

a) Show that the gradient of PQ is5

1−  ( 1 )  

 b) Show that the equation of PQ is x + 5y -7 = 0. ( 2 )  

c) Derive the equation of the line perpendicular to PQ passing through R. ( 2 ) 

d) Show that the midpoint of PR is ( -2 , 0 ). ( 1 ) 

e) What is the length of PQ? ( 1 )  

f) What is the perpendicular distance of R from PQ ? ( 1 ) 

g) What is the area of the triangle PQR? ( 1 )  

8. Show that the triangle whose sides satisfy 2x - y = 0 ,

x + 2y = 5 and x - 3y = 20 is both right-angled and isosceles. ( 5 ) 

9. Given that the point ( 4 , k ) lies on the line y = 3x - 7 , evaluate k. ( 1 ) 

10. Prove that the four lines listed below form a parallelogram. 

2x + 3y = 5 ( 3 ) 

y = 3x + 2 

6x-2y = 5

13

2+−=   x y  

11. Find the equation of the line that has an angle of inclination 135° and y-intercept of 2. ( 2 ) 

12. Find the equation of the line that is the perpendicular bisector  

of the interval joining ( 4 , 1 ) and ( 2 , 3 ) ( 3 ) 

13. Sketch y = sin x , (-180 ≤ x ≤ +180 ) making sure important points on 

the axes are labelled. ( 2 )