8/18/2019 Exercise Chapter 6

1/4

Page 1 of 4

1.  The vertices of a triangle are  P  (6, 1), Q (5, 6) and  R (m, -1). Given that the area of the

triangle is 31 unit2, find the values of m.

2. 

The points  P   (3m, m), Q  (t , u) and  R  (3t , 2u) lie on a straight line. Q divides  PR  in the

ratio of 3:2. Express t  in terms of u.

3. 

The equation of the straight lines CD and  EF  are 5 x +  y  –  4 = 0 and

. If CD and

 EF  are parallel, find the value of h.

4.  The straight line

  has a  y-intercept of 3 and is parallel to the straight line

 y + qx = 0. Determine the value of p and q.

5.  The equations of two straight lines

 and 7 y = 4 x + 21. Determine whether the

lines are perpendicular to each other.

6. 

The point  M  is (-3, 5) and the point  N  is (4, 7). The point  P  moves such that  PM : PN  = 2:3.

Find the equation of the locus of  P .

7.  Given that points  A (0, 2) and  B (6, 5). Find the equation of the locus of a moving point  P  

such that the triangle  APB always has a right angle at  P .

8. 

0

 y

 x

 R (0, -6 )

S  (12, 0)

Q

 P 

 

The diagram shows a straight line  PQ which meets a straight line  RS  at the point Q. The

 point P  lies on the  y-axis.a.

 

Write down the equation of  RS  in the intercept form.

 b.  Given that 2 RQ = QS , find the coordinates of Q.

c. 

Given that  PQ is perpendicular to  RS , find the  y-intercept of  PQ.

8/18/2019 Exercise Chapter 6

2/4

Page 2 of 4

9. 

0

 y

 x

 P 

 R (w, 0)

S  (4, -3)

Q (5, 5)

 

The diagram shows a trapezium  PQRS . Given that the equation of  PQ is 2 y  –   x  –  5 = 0,

find

a. 

The value of w. b.  The equation of  PS  and hence find the coordinates of  P .

c.  The locus of  M  such that triangle QMS  is always perpendicular at  M .

10. 

0

 y

 x

 P  (3, 2)

Q (4, 5)S  (7, 6)

T 

 

In the diagram,  PRS   and QRT   are straight lines. Given  R  is the midpoint of  PS   and

QR: RT  = 1:3, find

a.  The coordinates of  R.

 b. 

The coordinates of T .c. 

The coordinates of the point of intersection between lines  PQ and ST  produced.

8/18/2019 Exercise Chapter 6

3/4

Page 3 of 4

11. 

0

 y

 x

 K 

 M 

 L

 N  (10, 12)

 

The diagram shows a triangle  LMN  where  L is on the  y-axis. The equation of the straight

line  LKN  and  MK  are 2 y  –  3 x + 6 = 0 and 3 y +  x  –  13 = 0 respectively. Find

a. 

The coordinates of  K .

 b.  The ratio  LK : KN .

12. 

0

 y

 x

G M  P 

 E  (2, 4)

 

In the diagram, the equation of  FMG  is  y = -4. A point  P  moves such that its distance

from  E  is always half of the distance of  E  from the straight line  FG. Find

a.  The equation of the locus  P .

 b.  The x-coordinate of the point of intersection of the locus and the  x-axis.

8/18/2019 Exercise Chapter 6

4/4

Page 4 of 4

13. Diagram below shows a triangle OPQ. Point S  lies on the line  PQ.

0

 y

 x

Q

 P  (2, k )

S  (5, 3)

 

a.  A point Y  moves such that its distance from point S   is always 5 units. Find the

equation of the locus of Y .

 b.  It is given that the point  P  and point Q lie on the locus of Y . calculate

i.  The value of k .

ii. 

The coordinates of Q.

c.  Hence, find the area, in unit2 of triangle OPQ.