
Homework 1 Straight
Lines


Give answers to 2 decimal places




Your Score:
















Q1

Line l_{1} passes through the points A = ( 4, 12 ) and B = ( 3, 2 ).












a)

Find the gradient of l_{1}


m =





b)

Find the equation of l_{1} in the form y = m x + c.















y =


x +
















Line l_{2} is perpendicular to l_{1} and passes through B.












c)

Give the equation of line l_{2} in the form a x + b y + c = 0



where a > 0, b and c
are integers without common factors.














a =


b =


c =























Q2

The triangle ABC has vertices as follows:













A =

(2, 8)

B =

(4, 4)

C =

(4, 8)















Calculate:


















a)

The gradient of AB






b)

The gradient of BC






c)

The length of AB (2 d.p.)






d)

The length of BC (2.d.p.)






e)

Area of the triangle (nearest whole number)

























Q3

Line l_{1} passes through the points A = ( 5, 2 ) and B = ( 8, 3 ).












a)

Give the equation of line l_{1} in the form a x + b y + c = 0



where a > 0, b and c
are integers without common factors.














a =


b =


c =














b)

Line l_{2} is perpendicular to l_{1} and passes through ( 4, 6 ).



Find the equation of this new line:















y =


x +















c)

Find the point of intersection of these two lines.
Give x to 2 d.p.



Use your rounded answer to x when working out y.







x =


y =
























Q4)

Line l_{1} is given by the equation y = 5x  3.


Line l_{2} is perpendicular to l_{1} and passes through P = (7, 8).













a)

Write down the gradient of l_{2}






b)

Hence find the equation of l_{2}.



















y =


x +















c)

l_{1} and l_{2} cross the x axis at the points A and B
respectively:














x

y



x

y




A =




B =















d)

Calculate the length of the line PB,
answer to 2 d.p.














length PB =


























Q5)

Line l_{1} passes through the points A = ( 4, 6 ) and B = ( 7, 4 ).












a)

Give the equation of line l_{1} in the form a x + b y + c = 0



where a > 0, b and c
are integers without common factors.














a =


b =


c =














b)

M is
the midpoint of AB and l_{2} is perpendicular to AB and



passes through M.













Give the equation of line l_{2} in the form a x + b y + c = 0



where a > 0, b and c
are integers without common factors.














a =


b =


c =


