Question

When archeologists excavate a site, they mark it off with a coordinate grid so that they can easily

identify where artefacts are found and keep a record of the site forever. At the West Kennet Long
Barrow in England, a grave site back to 3600 BCE was found. There are three chambers at the
coordinates (7,9), (17, 33) and (-36,41). It has been said that they form an isosceles triangle with
height twice the length of its base.
Determine whether the statement is true. Justify your answer. Hint: An isosceles triangle has at
least two sides of equal side lengths.

Answer 1

To determine whether the statement that the three chambers at the West Kennet Long Barrow form an isosceles triangle is true, we need to first calculate the distances between each pair of chambers.

The distance between the chambers at coordinates (7,9) and (17,33) can be calculated using the distance formula:

distance = √((x2-x1)^2 + (y2-y1)^2)

Plugging in the coordinates, we get:

distance = √((17-7)^2 + (33-9)^2)

distance = √(10^2 + 24^2)

distance = √(100 + 576)

distance = √676

distance = 26

The distance between the chambers at coordinates (7,9) and (-36,41) can be calculated using the same formula:

distance = √((-36-7)^2 + (41-9)^2)

distance = √((-43)^2 + (32)^2)

distance = √(1849 + 1024)

distance = √2873

distance = 53.6

The distance between the chambers at coordinates (17,33) and (-36,41) can be calculated using the same formula:

distance = √((-36-17)^2 + (41-33)^2)

distance = √((-53)^2 + (8)^2)

distance = √(2809 + 64)

distance = √2873

distance = 53.6

Since the distance between the chambers at coordinates (7,9) and (17,33) is not equal to either of the distances between the other pairs of chambers, we can conclude that the statement is not true. The chambers do not form an isosceles triangle, as they do not have at least two sides of equal side lengths