O Level Physics

1. A is the point (5, 7) and B is the point (9, -1).

     (a) Find the length AB.

 

 

 

 

…………………………………………. [3]

     (b) Find the equation of the line AB.

 

 

 

 

 

…………………………………………. [3]

2. Find the gradient of the line that is perpendicular to the line .

 

 

 

 

…………………………………………. [2]

 

 

 

3. (a) A is the point and B is the point .

Find the equation of the line that passes through A and B.

Give your answer in the form   .

 

 

 

 

 

 

 

=  ………………………………………… [3]

     (b)  The line CD has equation   .

Find the gradient of a line that is perpendicular to the line CD.

 

 

…………………………………………. [1]

4. A line from the point is perpendicular to the line

The two lines meet at the point P.

 

Find the coordinates of P.

 

 

 

 

 

 

 

 

 

 

 

(……………,  …….……..) [5]

is the point and  is the point .

Find the equation of line

Give your answer in the form

 

 

 

=  ………………………………………… [2]

6. is the point  and  is the point .

is the midpoint of the line .

     (a) Find the coordinates of .

 

 

 

( …………………. ,  …………………. ) [1]

(b) (i) Find the gradient of the line .

 

 

 

 

…………………………………………. [2]

(ii) Write down the gradient of a line that is perpendicular to the line .

 

 

 

…………………………………………. [1]

7. is the point and  is the point  .

(a) Find the coordinates of the midpoint of AB.

 

 

(………………. ,……………….) [1]

(b) Line  is the locus of points that are equidistant from  and .

Find the equation of line .

 

 

 

 

 

 

 

 

 

 

…………………………………………. [4]

 

8. is a line segment joining and

     (a) B is the midpoint of the line segment

Find the coordinates of

 

 

(……….., ……….) [1]

     (b) The length of   is

Find the value of

 

 

 

 

 

…………………[2]

     (c) Find the equation of the line perpendicular to  that passes through .

Give your answer in the form .

 

 

 

 

 

 

 

 

 

 

 

 

= ………………………… [4]

9. Point is joined to point by a straight line.

(a) Find the coordinates of the midpoint of .

 

 

( …………………. , …………………. ) [1]

     (b) Find the gradient of the line .

 

 

 

 

…………………………………………. [2]

10. is the point and  is the point .

(a) Find the coordinates of the midpoint of the line PQ.

 

 

( …………………. , …………………. ) [1]

     (b) Find the equation of the line perpendicular to PQ which passes through the point P.

 

 

 

 

 

 

 

 

 

 

 

 

…………………………………………. [4]

11.(a) Write down the coordinates of the point where the graph of  crosses the  –

axis.

 

( ………………….. , …………………..) [1]

(b)  is the point  and  is the point .

Find the equation of the perpendicular bisector of the line .

Give your answer in the form

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

=  …………………………………… [5]

 

12. The line intersects the curve at the points A and B.

Find the coordinates of A and B.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A (  ………………… , ………………… )

B (  ………………… , ………………… ) [5]

 

 

13.    The diagram shows the graph of    and the point

The tangent from P touches the graph of  at the point

The values of  and  are integers.

 

(a) By drawing this tangent, find the value of a and the value of b.

 

 

=  ………………. ,   = ………………. [2]

(b) Find the equation of the tangent.

Give your answer in the form .

 

 

 

 

=  ………………………………………… [3]

 

14.(a)  is the point  and  is the point .

(i) Find the -coordinate of the midpoint of .

 

 

………………………….[1]

(ii) The line  has gradient .

Find an expression for  in terms of .

 

 

 

 

 

 

……………………..[3]

(b)  is the point  and  is the point .

is the point on  such that  = .

 

Find the coordinates of .

 

 

 

( …………………. , …………………. ) [3]