Question

1. a rectangular field has corners at (0, 0), (0, 4), (6, 0), and (6, 4). what is the length of the diagonal across the field?

a. 8 units
b. 6 units
c. 10 units
d. √52 units

Explanation:

Step1: Identify length and width

Length = 6 (difference in x - coordinates of two points), width = 4 (difference in y - coordinates of two points).

Step2: Apply Pythagorean theorem

For a right - triangle formed by the length, width and diagonal of the rectangle, if \(a = 6\), \(b = 4\) and \(c\) is the diagonal, then \(c^{2}=a^{2}+b^{2}\). So \(c=\sqrt{6^{2}+4^{2}}=\sqrt{36 + 16}=\sqrt{52}\).

Answer:

d. \(\sqrt{52}\) units