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

`9.91`

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 = √((x_2-x_1)^2 + (y_2-y_1)^2)\\d = √((1 - 1)^2 + (8-1)^2)\\d = √((0)^2 + (7)^2)\\d = √(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\\√(98) = c\\c \approx 9.91`