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Coordinate Geometry · Paper 1 — Free Maths AA SL Practice Questions

1FoundationSAQ-SEquation of a straight lines7 marksPaper 1~11 min

A straight line

L

passes through the point

A(2,\,5)

and has a gradient of

-3

(a)

Find the equation of

L

in the form

y = mx + c

. [2 marks]

(b)

Find the coordinates of the point where

L

crosses the

x

-axis. [2 marks]

(c)

A second line

M

has equation

y = 2x - 4

. Determine the coordinates of the point of intersection of

L

and

M

. [3 marks]

Solutions

2FoundationSAQ-SEquation of a straight lines5 marksPaper 1~8 min

The below shows a straight line

L

passing through points

A(0,\,4)

and

B(2,\,0)

(a)

Calculate the gradient of

L

. [2 marks]

(b)

Find the equation of

L

in the form

y = mx + c

. [1 mark]

(c)

A second line

M

has equation

y = x - 2

. Determine the coordinates of the point of intersection of

L

and

M

. [2 marks]

Solutions

3MasterySAQ-SEquation of a straight lines13 marksPaper 1~20 min

A line

L

passes through the points

A(-2,\,7)

and

B(4,\,-5)

(a)

Show that the equation of line

L

y = -2x + 3

. [3 marks]

(b)

Find the coordinates of the point

P

where line

L

intersects the line

y = x

. [2 marks]

(c)

A second line

M

passes through

P

and is perpendicular to

L

. Determine whether

M

passes through the point

C(3,\,4)

. [3 marks] Total: [8 marks]

Solutions

4ChallengeSAQ-LEquation of a straight lines8 marksPaper 1~12 min

A farmer is designing a triangular field

ABC

for grazing sheep. The vertices are located at

A(2,\,1)

B(8,\,5)

, and

C(4,\,7)

, where coordinates are in kilometres.

(a)

Determine the equation of the straight line that passes through

A

and is perpendicular to

BC

. Give your answer in the form

ax + by + c = 0

, where

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

. [4 marks]

(b)

The line found in part (a) meets

BC

at point

D

. Determine the coordinates of

D

. [2 marks]

(c)

Show that

D

divides

BC

in the ratio

BD:DC = 4:1

, and hence determine the ratio of the area of triangle

ABD

to the area of triangle

ABC

. [2 marks]

Solutions

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