In this issue of Math in the News we join the investigation in the missing flight MH370. We discuss the details of the flight and what we know so far. Using coordinate geometry, students can explore how experts narrow down the search area.

1. Math in the News
Issue 98
THE SEARCH FOR
MISSING FLIGHT MH370

2. • Malaysian Airlines Flight 370 was
a passenger flight scheduled to
travel from Kuala Lumpur
International Airport in Malaysia to
Beijing Capital International Airport
on March 8, 2014.
• The flight was last heard from
March 8 at 1:20 Malaysian time.
• The aircraft was carrying 12 crew
members and 227 passengers
from 14 nations.
THE SEARCH FOR FLIGHT MH370

3. The intended
flight path
was direct,
expected to
fly Northeast
until it landed
in Beijing.
THE SEARCH FOR FLIGHT MH370

4. However,
information from
Malaysian military
satellites indicate
that the flight veered
West shortly after
takeoff.
THE SEARCH FOR FLIGHT MH370

5. THE SEARCH FOR FLIGHT MH370
Select the image to watch a BBC video on the flight path and
the search for MH370
http://www.bbc.com/news/world-asia-26503141

6. Authorities confirmed
that the airplane crashed
somewhere in the Indian
Ocean and have begun
their search in the vast
sea. Air satellites have
detected some debris in
the water and satellite
“pingers” have been
dropped into the ocean
to detect signals from the
plane’s black box.
THE SEARCH FOR FLIGHT MH370
Search area for flight MH370

7. Based on the
location of the
pings and debris
fields,
mathematicians
are attempting to
narrow down the
search area.
Coordinate
geometry allows
us to map the
search area.
THE SEARCH FOR FLIGHT MH370
French satellite imagery showing
potential debris on March, 23, 2014

8. Coordinate geometry
maps coordinates on a
coordinate plane, such
as the one shown on the
right. The plan has a
horizontal axis (x) and a
vertical axis (y).
Coordinates are written
in (x,y) format where the
x indicates left/right
movement and the y
indicates up/down
movement.
THE SEARCH FOR FLIGHT MH370
x
y
(15,10)

9. If we have enough
coordinates, we
can map the area.
This is the method
authorities are
using to find
MH370. Let’s try an
example.
THE SEARCH FOR #MH370
A
DC
B

10. The Surveyor’s Area Formula, also known as
the Shoelace Formula, can be used to find the
area of any polygon on a grid. Those looking
for flight MH370 will use this technique to
determine the search area. The following
shows the area for a quadrilateral, but the
formula can be used for any polygon.
THE SEARCH FOR FLIGHT MH370
Continue to see how to use the formula
and how it got its name…

11. The Surveyor’s Formula was first used for land surveyors to
estimate the an area of land using coordinates. It is derived
using determinants corresponding to the vectors of the edges
of a polygon.
Determinants =
Based on determinants, the formula is written as
After the determinants are multiplied out, the formula can be re-
written for quadrilaterals as:
THE SEARCH FOR FLIGHT MH370

12. To use the Surveyor’s Formula, we first need to lay out the
coordinates in a table as they sit counterclockwise
THE SEARCH FOR FLIGHT MH370
Coordinate (x, y)
A (15,10)
B (5, 15)
C (-10, -10)
D (20, -10)

13. THE SEARCH FOR FLIGHT MH370
Coordinate x y
A 15 10
B 5 15
C -10 -10
D 20 -10
A 15 10 The formula got its second name, the Shoelace formula,
because of how it looks when you cross multiply!
Now, we can plug the points into the
formula. First, let’s do the math inside the
absolute value sign…
(15 • 15) + (5 • -10) + (-10 • -10) + (20 • 10)
– (5 • 10) – (-10 • 15) – (20 • -10) – (15 • -10) =
(225) + (-50) + (100) + (200)
– (50) – (-150) – (-200) – (-150) = 925
Now, we can finish the equation…

14. THE SEARCH FOR FLIGHT MH370
The area of the
polygon on the
coordinate plane is
462.5 square units.
1/2│925│= 462.5

15. With the same
method, you can use
the coordinates of
the debris to find
one of the potential
search areas. The
world is mapped
much like a
coordinate plane,
where East and
West represent the
x-axis and North and
South represent the
y-axis.
THE SEARCH FOR FLIGHT MH370

16. • Consider the following questions:
• In what units is the search area measured?
• How does the depth of the ocean impact
the difficulty of the search?
• Take a look at this video update on the
search for flight MH370. How does this
impact the search? Can we still use the
Surveyor’s Formula with the new search
method?
THE SEARCH FOR FLIGHT MH370