Question

Alana is writing a coordinate proof to show that the diagonals of a square are congruent. She starts by assigning coordinates to a square as shown. Then she uses the coordinates to write and simplify expressions for the lengths of the diagonals.

What is the length of one of the diagonals of the square?

Answer 1

`\sf 6√(2) units`

Explanation:

A diagonal in a square is a line segment that joins two non-adjacent vertices of the square. A square has two diagonals, and they are both equal in length and perpendicular to each other.

In order to find length of diagonal let's take any diagonal points (0,6) and (6,0) or (0,0) and (6,6).

I will choose coordinate (0,0) and (6,6).

Now.

Using distance formula:

The distance formula is used to calculate the distance between two points in a coordinate plane. The formula is as follows:

`\sf distance = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

where:

(x1, y1) and (x2, y2) are the coordinates of the two points

In this case, we are calculating the distance between the points (0, 0) and (6, 6).

Substituting these values into the distance formula, we get:

`\sf distance = √((6 - 0)^2 + (6 - 0)^2)`

`\sf distance = √(6^2 + 6^2)`

`\sf distance = √(36+36)`

`\sf distance = √(72)`

`\sf distance = 6√(2)`

Therefore, length of one of the diagonals of the square is
`\sf 6√(2) units`