Question

The vertices of a square are p(1, 1), q(1, 8), r(8, 8) and s(8, 1).what is the length of the diagonal

Answer 1

Answer:

$9.91$

Step-by-step explanation:

Since we know the shape is a square, all vertices should be the same length. Find the length of one vertex, by finding the distance between any two points. The following equation uses points $p$ and $q$:

$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\\d = \sqrt{(1 - 1)^2 + (8-1)^2}\\d = \sqrt{(0)^2 + (7)^2}\\d = \sqrt{49}\\d = 7$

Since the distance is 7, for all sides use the Pythagorean theorem to find the diagonal:

$a^2 + b^2 = c^2\\7^2 + 7^2 = c^2\\49 + 49 = c^2\\98 = c^2\\\sqrt{98} = c\\c \approx 9.91$