Three pirates - Calico Jack, Black Beard, and Long John Silver - are searching for a pot of gold located at the coordinate point (0,0). Their locations are Calico Jack (-4,5), Black Beard (-7,-1), and Long John Silver (6,2). Using the distance formula, it is determined that Calico Jack has the shortest distance of 41 km to the pot of gold, making him the closest pirate.

1. COORDINATE
GEOMETRY
Calculating Distance

2. Who is closest to the pot of gold?
Three pirates are on a
quest to find the pot of
gold, situated at the origin
{0,0}.
The pirates are located at
the following points:
Calico Jack – { -4 , 5 }
Black Beard – { -7 , -1 }
Long John Silver – { 6 , 2 }
The measurements are in
kilometres.
Who is the closest?

3. Who is closest to the pot of gold?
Three pirates are on a
quest to find the pot of
gold, situated at the origin
{0,0}.
The pirates are located at
the following points:
Calico Jack – { -4 , 5 }
Black Beard – { -7 , -1 }
Long John Silver – { 6 , 2 }
Who is the closest?

4. Who is closest to the pot of gold?
Use the formula (based on
Pythagoras’ theorem)
C – { -4 , 5 }
O–{0,0}
Distance = (x2 - x1 )2 + (y2 - y1 )2

5. Who is closest to the pot of gold?
C – { -4 , 5 }
O–{0,0}
Distance = (x2 - x1 )2 + (y2 - y1 )2
Distance = (0 - -4)2 + (0 - 5)2
= (16 + 25)
= 41
Distance for Calico Jack to gold is 6.4km (to 1 dp) or 41 km

6. Who is closest to the pot of gold?
Calico Jack – { -4 , 5 }
C = 41 km
Black Beard – { -7 , -1 }
B = (0 - -7)2 + (0 - -1)2
B = (49 +1)
Distance = (x2 - x1 ) + (y2 - y1 )
2
2
B = 50 km
Long John Silver – { 6 , 2 }
L = (0 - 6)2 + (0 - 2)2
Long John Silver is the closest to the Pot
of gold at
40 km
L = (36 + 4)
L = 40 km

7. Dragon’s Revenge
The computer game “Dragon’s Revenge” uses coordinates
to place objects in the game.
Dracon the dragon, who is near death, can only fire his
fireball a distance of 6 metres. Three attackers are in view.
He cannot afford to waste any fireballs. Dracon is situated
at the point (5,4)
The soldiers are placed at
A (8,7)
B (2,-1)
C (9,0)
Can Dracon kill all the soldiers? Show all your working.

8. Dragon’s Revenge
• Distance AD
A
D
C
B
AD = (8 - 5)2 + (7 - 4)2
AD = (9 + 9
AD = 18
• Distance CD
CD = (2 - 5)2 + (-1- 4)2
CD = 9 + 25
CD = 34
• Distance BD
BD = (9 - 5)2 + (0 - 4)2
BD = 16 +16
BD = 32