Question

Suppose two adjacent endpoint of a rotated square are located at (-4, -6) and (5, -1) on the coordinates axes. What is the length of the side of the square?

Answer 1

To find the side length of the square, we use the Pythagorean theorem on the distance between the two given points, resulting in approximately 10.3 units.

Step-by-step explanation:

The student has provided two adjacent endpoints of a rotated square and is asking for the length of the side of the square. To find this, we calculate the distance between the two points, which is the length of one side of the square since these points are endpoints of the square. The distance is calculated using the Pythagorean theorem:

Distance = √((x2-x1)² + (y2-y1)²)

Substituting the provided coordinates (-4, -6) and (5, -1), we get:

Distance = √((5 - (-4))² + (-1 - (-6))²)
= √((5 + 4)² + (-1 + 6)²)
= √(9² + 5²)
= √(81 + 25)
= √106
= 10.3 (to three significant figures)

The length of the side of the square is therefore approximately 10.3 units.

Answer 2

To find the length of the side of the square, we just need to find the distance between the two endpoints. This problem can quickly be solved by using the distance formula, but for those who are not familiar with it, we can simply solve it by analyzing a triangle.

Take a look at the diagram below. We are interested in x. To find this we have created a right triangle. The horizontal component is just the distance between the x coordinates of the two points while the vertical component is the distance between the y coordinates.

The horizontal component is 9 and the vertical component is 5. We can now get x by using the pythagorean theorem:


`x^(2)= 9^(2) + 5^(2) =81+25=106`

`x= √(106)` which is approximately equal to 10.30 units.

ANSWER: The length of the side of the square measures 10.30 units.