Graphs - The Cartesian Plane

a - answer s - solution v - video d - discussion

Question 1

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

a) a

$A(2,1)$

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$A$ is 2 units to the right of and 1 unit above the origin so point $A$ is $(2,1)$

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b) a

$B(1,2)$

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$B$ is 1 unit to the right of and 2 units above the origin so point $B$ is $(1,2)$

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c) a

$C(4,2)$

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$C$ is 4 units to the right of and 2 units above the origin so point $C$ is $(4,2)$

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d) a

$D(4,4)$

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$D$ is 4 units to the right of and 4 units above the origin so point $D$ is $(4,4)$

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Question 2

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

a) a

$A(0,0)$

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$A$ is at the origin (no units above or to the right of the origin) so point $A$ is $(0,0)$

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b) a

$B(-2,1)$

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$B$ is 2 units to the left of and 1 unit above the origin so point $B$ is $(-2,1)$

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c) a

$C(-2,3)$

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$C$ is 2 units to the left of and 3 units above the origin so point $C$ is $(-2,3)$

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d) a

$D(-3,2)$

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$D$ is 3 units to the left of and 2 units above the origin so point $D$ is $(-3,2)$

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Question 3

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

a) a

$A(1,-1)$

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$A$ is 1 unit to the right of and 1 unit below the origin so point $A$ is $(1,-1)$

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b) a

$B(3,-2)$

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$B$ is 3 units to the right of and 2 units below the origin so point $B$ is $(3,-2)$

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c) a

$C(1,-3)$

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$C$ is 1 unit to the right of and 3 units below the origin so point $C$ is $(1,-3)$

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d) a

$D(4,-3)$

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$D$ is 4 units to the right of and 3 units below the origin so point $D$ is $(4,-3)$

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Question 4

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

a) a

$A(-1,-2)$

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$A$ is 1 unit to the left of and 2 unit below the origin so point $A$ is $(-1,-2)$

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b) a

$B(-2,-3)$

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$B$ is 2 units to the left of and 3 units below the origin so point $B$ is $(-2,-3)$

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c) a

$C(-3,-2)$

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$C$ is 3 units to the left of and 2 units below the origin so point $C$ is $(-3,-2)$

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d) a

$D(-3,-3)$

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$D$ is 3 units to the left of and 3 units below the origin so point $D$ is $(-3,-3)$

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Question 5

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

a) a

$A(2,2)$

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$A$ is 2 units to the right of and 2 units above the origin so point $A$ is $(2,2)$

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b) a

$B(-3,2)$

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$B$ is 3 units to the left of and 2 units above the origin so point $B$ is $(-3,2)$

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c) a

$C(0,0)$

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$C$ is at the origin (no units above or to the right of the origin) so point $C$ is $(0,0)$

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d) a

$D(2,-3)$

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$D$ is 2 units to the right of and 3 units below the origin so point $D$ is $(2,-3)$

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Question 6

Copy or print the Cartesian Plane below and plot on the points

a) $A(1,2)$ a

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b) $B(4,5)$ a

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c) $C(0,3)$ a

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d) $D(7,1)$ a

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e) $E(8,5)$ a

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Question 7

Copy or print the Cartesian Plane below and plot on the points

a) $A(-4,3)$ a

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b) $B(-5,0)$ a

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c) $C(6,-3)$ a

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d) $D(4,-7)$ a

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e) $E(0,-6)$ a

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f) $F(-2,2)$ a

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Question 8

Copy or print the Cartesian Plane below and plot on the points

a) $A(-2,-3)$ a

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b) $B(-6,-4)$ a

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c) $C(-4,-0)$ a

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d) $D(-3,-7)$ a

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e) $E(0,-4)$ a

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f) $F(-7,-7)$ a

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g) $G(0,0)$ a

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Question 9

Identify which quadrant the following points are in

a) $A(4,5)$ a

Quadrant $1$

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b) $B(-5,2)$ a

Quadrant $2$

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c) $C(-2,-2)$ a

Quadrant $3$

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d) $D(8,-4)$ a

Quadrant $4$

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e) $E(5,-4)$ a

Quadrant $4$

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f) $F(-4,7)$ a

Quadrant $2$

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g) $G(8,20)$ a

Quadrant $1$

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h) $H(-5,-6)$ a

Quadrant $3$

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i) $I(-4,17)$ a

Quadrant $2$

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j) $J(15,-22)$ a

Quadrant $4$

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k) $K(0,1)$ a

Does not lie in any quadrants. It lies on the $y$-axis

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l) $L(4,0)$ a

Does not lie in any quadrants. It lies on the $x$-axis

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m) $M(0,0)$ a

Does not lie in any quadrants. It lies on the origin

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Question 10

Copy or print the Cartesian Plane below and plot on the points in order. Join them up to form a picture!

a) $A(2,2)$, $B(2,5)$, $C(4,7)$, $D(6,5)$, $E(6,2)$ a

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b) $A(-5,-3)$, $B(-5,3)$, $C(-7,3)$, $D(-4,6)$, $E(-1,3)$, $F(-3,3)$, $G(-3,-3)$ a

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c) $A(5,-6)$, $B(-1,1)$, $C(5,7)$, $D(2,7)$, $E(-1,4)$, $F(-1,7)$, $G(-4,7)$ $H(-4,-6)$ $I(-1,-6)$ $J(-1,-3)$ a

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Question 1

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

Question 2

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

Question 3

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

Question 4

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

Question 5

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

Question 6

Copy or print the Cartesian Plane below and plot on the points

a) $A(1,2)$

b) $B(4,5)$

c) $C(0,3)$

d) $D(7,1)$

e) $E(8,5)$

Question 7

Copy or print the Cartesian Plane below and plot on the points

a) $A(-4,3)$

b) $B(-5,0)$

c) $C(6,-3)$

d) $D(4,-7)$

e) $E(0,-6)$

f) $F(-2,2)$

Question 8

Copy or print the Cartesian Plane below and plot on the points

a) $A(-2,-3)$

b) $B(-6,-4)$

c) $C(-4,-0)$

d) $D(-3,-7)$

e) $E(0,-4)$

f) $F(-7,-7)$

g) $G(0,0)$

Question 9

Identify which quadrant the following points are in

a) $A(4,5)$

b) $B(-5,2)$

c) $C(-2,-2)$

d) $D(8,-4)$

e) $E(5,-4)$

f) $F(-4,7)$

g) $G(8,20)$

h) $H(-5,-6)$

i) $I(-4,17)$

j) $J(15,-22)$

k) $K(0,1)$

l) $L(4,0)$

m) $M(0,0)$

Question 10

Copy or print the Cartesian Plane below and plot on the points in order. Join them up to form a picture!

a) $A(2,2)$, $B(2,5)$, $C(4,7)$, $D(6,5)$, $E(6,2)$

b) $A(-5,-3)$, $B(-5,3)$, $C(-7,3)$, $D(-4,6)$, $E(-1,3)$, $F(-3,3)$, $G(-3,-3)$

c) $A(5,-6)$, $B(-1,1)$, $C(5,7)$, $D(2,7)$, $E(-1,4)$, $F(-1,7)$, $G(-4,7)$ $H(-4,-6)$ $I(-1,-6)$ $J(-1,-3)$

Answers

Question 1

a) $A(2,1)$

b) $B(1,2)$

c) $C(4,2)$

d) $D(4,4)$

Question 2

a) $A(0,0)$

b) $B(-2,1)$

c) $C(-2,3)$

d) $D(-3,2)$

Question 3

a) $A(1,-1)$

b) $B(3,-2)$

c) $C(1,-3)$

d) $D(4,-3)$

Question 4

a) $A(-1,-2)$

b) $B(-2,-3)$

c) $C(-3,-2)$

d) $D(-3,-3)$

Question 5

a) $A(2,2)$

b) $B(-3,2)$

c) $C(0,0)$

d) $D(2,-3)$

Question 6

Question 7

Question 8

Question 9

a) Quadrant $1$

b) Quadrant $2$

c) Quadrant $3$

d) Quadrant $4$

e) Quadrant $4$

f) Quadrant $2$

g) Quadrant $1$

h) Quadrant $3$

i) Quadrant $2$

j) Quadrant $4$

k) Does not lie in any quadrants. It lies on the $y$-axis

l) Does not lie in any quadrants. It lies on the $x$-axis

m) Does not lie in any quadrants. It lies on the origin

Question 10

Question 1

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

Question 2

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

Question 3

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

Question 4

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

Question 5

Find the coordinates of $A$, $B$, $C$ and $D$ on the following Cartesian plane

Question 6

Copy or print the Cartesian Plane below and plot on the points

a) $A(1,2)$

b) $B(4,5)$

c) $C(0,3)$

d) $D(7,1)$

e) $E(8,5)$

Question 7

Copy or print the Cartesian Plane below and plot on the points

a) $A(-4,3)$

b) $B(-5,0)$

c) $C(6,-3)$

d) $D(4,-7)$

e) $E(0,-6)$

f) $F(-2,2)$

Question 8

Copy or print the Cartesian Plane below and plot on the points

a) $A(-2,-3)$

b) $B(-6,-4)$

c) $C(-4,-0)$

d) $D(-3,-7)$

e) $E(0,-4)$

f) $F(-7,-7)$

g) $G(0,0)$

Question 9

Identify which quadrant the following points are in

a) $A(4,5)$

b) $B(-5,2)$

c) $C(-2,-2)$

d) $D(8,-4)$

e) $E(5,-4)$

f) $F(-4,7)$

g) $G(8,20)$

h) $H(-5,-6)$

i) $I(-4,17)$

j) $J(15,-22)$

k) $K(0,1)$

l) $L(4,0)$

m) $M(0,0)$

Question 10

Copy or print the Cartesian Plane below and plot on the points in order. Join them up to form a picture!

a) $A(2,2)$, $B(2,5)$, $C(4,7)$, $D(6,5)$, $E(6,2)$

b) $A(-5,-3)$, $B(-5,3)$, $C(-7,3)$, $D(-4,6)$, $E(-1,3)$, $F(-3,3)$, $G(-3,-3)$

c) $A(5,-6)$, $B(-1,1)$, $C(5,7)$, $D(2,7)$, $E(-1,4)$, $F(-1,7)$, $G(-4,7)$ $H(-4,-6)$ $I(-1,-6)$ $J(-1,-3)$

Answers

Question 1

a) $A(2,1)$
b) $B(1,2)$
c) $C(4,2)$
d) $D(4,4)$

Question 2

a) $A(0,0)$
b) $B(-2,1)$
c) $C(-2,3)$
d) $D(-3,2)$

Question 3

a) $A(1,-1)$
b) $B(3,-2)$
c) $C(1,-3)$
d) $D(4,-3)$

Question 4

a) $A(-1,-2)$
b) $B(-2,-3)$
c) $C(-3,-2)$
d) $D(-3,-3)$

Question 5

a) $A(2,2)$
b) $B(-3,2)$
c) $C(0,0)$
d) $D(2,-3)$

Question 6

Question 7

Question 8

Question 9

a) Quadrant $1$
b) Quadrant $2$
c) Quadrant $3$
d) Quadrant $4$
e) Quadrant $4$
f) Quadrant $2$
g) Quadrant $1$
h) Quadrant $3$
i) Quadrant $2$
j) Quadrant $4$
k) Does not lie in any quadrants. It lies on the $y$-axis
l) Does not lie in any quadrants. It lies on the $x$-axis
m) Does not lie in any quadrants. It lies on the origin

Question 10

Solutions

Question 1

a) $A$ is 2 units to the right of and 1 unit above the origin so point $A$ is $(2,1)$

b) $B$ is 1 unit to the right of and 2 units above the origin so point $B$ is $(1,2)$

c) $C$ is 4 units to the right of and 2 units above the origin so point $C$ is $(4,2)$

d) $D$ is 4 units to the right of and 4 units above the origin so point $D$ is $(4,4)$

Question 2

a) $A$ is at the origin (no units above or to the right of the origin) so point $A$ is $(0,0)$

b) $B$ is 2 units to the left of and 1 unit above the origin so point $B$ is $(-2,1)$

c) $C$ is 2 units to the left of and 3 units above the origin so point $C$ is $(-2,3)$

d) $D$ is 3 units to the left of and 2 units above the origin so point $D$ is $(-3,2)$

Question 3

a) $A$ is 1 unit to the right of and 1 unit below the origin so point $A$ is $(1,-1)$

b) $B$ is 3 units to the right of and 2 units below the origin so point $B$ is $(3,-2)$

c) $C$ is 1 unit to the right of and 3 units below the origin so point $C$ is $(1,-3)$

d) $D$ is 4 units to the right of and 3 units below the origin so point $D$ is $(4,-3)$

Question 4

a) $A$ is 1 unit to the left of and 2 unit below the origin so point $A$ is $(-1,-2)$

b) $B$ is 2 units to the left of and 3 units below the origin so point $B$ is $(-2,-3)$

c) $C$ is 3 units to the left of and 2 units below the origin so point $C$ is $(-3,-2)$

d) $D$ is 3 units to the left of and 3 units below the origin so point $D$ is $(-3,-3)$

Question 5

a) $A$ is 2 units to the right of and 2 units above the origin so point $A$ is $(2,2)$

b) $B$ is 3 units to the left of and 2 units above the origin so point $B$ is $(-3,2)$

c) $C$ is at the origin (no units above or to the right of the origin) so point $C$ is $(0,0)$

d) $D$ is 2 units to the right of and 3 units below the origin so point $D$ is $(2,-3)$