COORDINATE GEOMETRY

 

Question 1

                                      Solution

 

Question2

Solution

 

Question 3                             

            

            Solution

 

Question 4

 

                                   Solution

                 

 

Question 5

Find the equation of the perpendicular at point (4,3) to the line  (UME 2005,             Question 32)

 

Solution

 

            Question 6

Find the coordinate of the midpoint of the line joining (3,4) and (–1,10) (UME 2005,     Question 32)

Solution

 

Question 7

Find  the mid-point of the line joining D (–3, 5) and  Q(5 ,– 3) (UME 2004,Question32)

Solution

Question 8

Find the value of  if  

 (UME 2004, Question 31)

 

Solution

                 

 

Question 9

Find the value of p, if the line passes through ( – 1, –p) and (–2p, 2) is parallel to

the line 2y +8x –17 = 0 (UME 2003, Question 27)

 

Solution

 

          

 

 

 

           Question 10

Find the coordinate of the midpoint of x and y intercept  (UME 2002, Question 36)

 

 

 

 

 

 

 

 

 

 

 

 

Solution

 

Intercept on y – axis, set x = 0

            Question 11

The straight lines makes an angle of 30^o with the positive x – axis with cut the y – axis    at y =5. Find the equation of the straight line

 

Solution

   

 

 

 

 

 

 

 

 

                                         

                                                

 

            Question 12

Solution

 

 

 

 

 

 

           

 

             Question 13

Find the value of P if the line joining (P,4) and (6 ,– 2) is perpendicular to the line joining (2,P) and ( – 1, 3)

 

            Solution

 

 

 

 

 

 

 

 

 

 

         

 

Question 14

                                   Solution

 

Question 15

Find a positive value of  if the coordinate of the center of a circle  is

Solution

          

 

Question 16

           

Solution

 

Question 17

if  the distance between the point (x,3) and ( –x, 2) is 5, find x (UME 1998, Question 32)

 

Solution

 

 

 

 

 

 

 

 

 

 

 

Question 18

The mid-point of the segment of the line y =4x + 3 which lies between  x – axis and y – axis (UME 1998, Question 33)

 

Solution

 

 

 

 

 

 

 

 

 

 

 

 

Intercept on y – axis, set x = 0

y =4(0)+3 =3

Coordinate of A =(0, 3)

Intercept on x – axis, set y = 0

0= 4x + 3,  x = –3/4

Coordinate of B = (–3/4, 0)

     

 

Question 19

The angle between the positive horizontal axis and  a given line is 135^o, find the equation of the line if it passes through the point (2,3) (UME 1997, Question 23)

Solution

 

 

 

 

 

 

 

 

 

         

 

Question 20

Find the distance between the point Q(4,3) and the point common to the line 2x – y  and x + y (UME 1997, Question 34)

 

Solution

 

 

 

 

 

 

 

           

 

Question 21

If M (4,q) is the mid – point of the line L (p, –2) and N(q,p), find the value of p and   q (UME 1994, Question 35)

 

Solution

 

 

 

                                         

 

Question 22

 

 

 

 

 

 

 

 

 

 

The equation of the line in the graph above is (UME 1994, Question 36)

 

Solution

               

Question 23

What is the perpendicular distance of a point (2,3) from the line 2x – 4y +3 = 0

 

Solution

          

Question 24

Find the equation of the line through (5,7) parallel to the line 7x + 5y =12

(UME 1992, Question 32)

 

Solution

 

 

Question 25

Find the gradient of a line which is perpendicular to the line with the equation

3x +2y +1 = 0   (UME 2008, Question 32 set U03, type A)

 

Solution

Transform the given equation

l₁: 3x + 2y + 1 = 0 to the form y = mx+ c

l₁: 3x + 2y + 1 = 0

          

The slope of l₁is m₁ =

For two lines to be

The gradient of the line which will be perpendicular to 3x +2y +1 = 0 is 2/3

Answer: Option B

 

Question 26

Calculate the distance between point L (–1 – 6) and M(–3, –5) 

             (UME 2008, Question 32 set U03, type A)

 

Solution

            Answer: Option A

 

Question 27

Find the acute angle between the straight lines y = x and y =

(a)  15^o  (b)  30^o   (c)  45^o  (d)  60^o (UME 2009, Question 24 set U03)

 

 

Solution

Answer: Option A