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Coordinate Geometry · Paper 3 — Free Maths AA HL Practice Questions

1ChallengeLAQEquation of a straight lines7 marksPaper 3~11 min

A line

L_1

passes through the points

A(1,3)

and

B(5,11)

. A second line

L_2

is perpendicular to

L_1

and passes through the point

C(2,-1)

. A third line

L_3

is the reflection of

L_2

in the line

y = x

(a)

Show that the equation of

L_1

y = 2x + 1

. [3 marks]

(b)

(i) Find the equation of

L_2

in the form

ax + by + c = 0

, where

a, b, c \in \mathbb{Z}

. [3 marks]
(ii) Find the coordinates of the point

D

where

L_1

and

L_2

intersect. [2 marks]

(c)

L_3

intersects

L_1

at point

F

. Determine the coordinates of

F

and hence show that

D

C

, and

F

are not collinear. [2 marks]

Solutions

Questions 2-11

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