mathematics-straight-line-graphs.pdf

8/18/2019 Mathematics-Straight-Line-Graphs.pdf

1/3

www.hscintheholidays.com.au All rights reserved ©

STRAIGHT LINE GRAPHS

1) Find the exact distance between points A(3,-1) and B(-2,-6).

2) Show that A(1,4), B(-1,-1) and C(4,1) are the vertices of an isosceles triangle.

3) Find the midpoint of (3,6) and (-1,4).

4) A circle, centre (2,3) has the point X(6,-1) on its circumference. Find(a) the coordinates of the other point on the circle with diameter through X

(b) the length of the diameter, to one decimal place.

5) Find the gradient of the straight line that passes through (3,-5) and (1,-7).

6) Prove that points A(4,5), B(7,3) and C(13,-1) are collinear.

7) Find the exact gradient of the straight line that makes an angle of 1500 with the

x-axis in the positive direction.

8) What is the gradient of the straight line with equation 2 x + 3 y - 5 = 0?

9) Find the equation of the straight line with gradient 3 and passing through (1,2).

10) What is the equation of the straight line that passes through (3,2) and (-1,5)?

11) A straight line has x-intercept 1 and y-intercept -2. Find its equation.

12) Show that the straight lines y = 3 x - 1 and 3 x - y + 4 = 0 are parallel.13) Find the equation of the straight line that passes through (3,4) and is parallel to the

line 2 x - 5 y + 1 = 0.

14) Prove that the straight lines 6 x + 5 y + 1 = 0 and 5 x - 6 y - 12 = 0 are perpendicular.

15) Find the equation of the straight line through (0,4) that is perpendicular to the line

4 x - 3 y + 2 = 0.

16) Find the point of intersection of the lines x + 3 y +2 = 0 and 3 x - 2 y - 16 = 0.

17) Show that the straight lines with equations x + 2 y +2 = 0, 5 x + 3 y - 4 = 0 and

3 x - 2 y - 10 = 0 are concurrent.

18) Find the equation of the straight line passing through (-3,-2) and passing through

the intersection of 2 x - 5 y - 3 = 0 and 3 x - 4 y - 8 = 0.

19) Find the perpendicular distance (in exact form) from the point (2,5) to the line

3 x - 2 y - 1 = 0.

20) Show that the points A(-1,3), B(2,1), C(1,-3) and D(-2,-1) are the vertices of a

parallelogram.

21) (a) Plot points A(2,1) and B(-2,-3) on a number plane.

(b) Find the midpoint, C, of AB.

(c) Show that the line through C perpendicular to AB has equation x + y + 1 = 0.

(d) Show that this line passes through D(-3,2).

(e) Find the area of triangle ABD.

(f) Find the point E so that AEBD is a rhombus.

22) (a) Plot points A(-1,1), B(0,4) and C(1,3) on a number plane.(b) Show that the gradient of BC is equal to the gradient of AO, where O is the

origin.

(c) Show that BC = AO.

(d) What shape best describes the figure OABC?


2/3


ANSWERS

1) 50 5 2 units

2) AB = BC = 29 , AC = 18

3) (1,5)

4) (a) (-2,7) (b) 11.3 units

5) 1

6) Gradient AB = gradient BC = 2

3

7) - 1

3

8) 2

3

9) 3 x - y - 1 = 0

10) 3 x + 4 y - 17 = 0

11) 2 x - y - 2 = 0

12) Both gradients = 313) 2 x - 5 y + 14 = 0

14) 6

5

5

61

15) 3 x+ 4 y - 16 = 0

16) (4,-2)

17) All intersect at (2,-2)

18) 3 x - 7 y - 5 = 0

19)5

13 units

20) Gradient AB=Gradient CD = 2

3, Gradient AD=Gradient BC = 4

21) (a)

y

x

1

4

3

2

1

32-1

-2

-1

-3

-4

-2-3

A

C

B

D

E

(b) C = (0,-1)


3/3


(c) AB has gradient 1, so perpendicular line has gradient -1.

y - (-1) = -1( x - 0)

y + 1 = - x

x + y + 1 = 0

(d) Substitute (-3,2) into equation. LHS = RHS = 0

(e) 12 units2

(f) E = (3,-4)

22) (a)

y

x

1

4

3

2

1

32-1

-2

-1

-3

-4

-2-3

A

C

B

O

(b) Both gradients are -1

(c) BC = AO = 2

(d) Parallelogram

mathematics-straight-line-graphs.pdf

Documents