An archaeologist has discovered various items at a site - Junior Cycle Mathematics - Question 11 - 2013

Since each square represents 1 m² and the grid is 10 squares by 10 squares:

Total area = $10 \times 10 = 100 \, m^{2}$.

By inspecting the grid, the item nearest to the tile (T) is the ring (R).

Using the distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Where:

• B = (2, 7)
• S = (2, 1)

Calculating: $d = \sqrt{(2 - 2)^2 + (1 - 7)^2} = \sqrt{0 + 36} = 6$

The slope (m) can be calculated using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where:

• P = (7, 1)
• B = (2, 7)

Calculating: $m = \frac{7 - 1}{2 - 7} = \frac{6}{-5} = -\frac{6}{5}$