Square ABCD has vertices A(-2,-3), B(4,-1), C(2,5), and D(-4,3). What is the length of a side of the square?

Question

Square ABCD has vertices A(-2,-3), B(4,-1), C(2,5), and D(-4,3). What is the length of a side of the square?

Answer 1

2+4=6=b

3-1=2=a

a^2+b^2=c^2

4+36=40^.5=6.3245.........

Answer 2

To elaborate on the previous poster's explanation: you need to use the distance formula to find the distance from two of the vertices of the square. The distance formula is as follows:

√(x₂-x₁)²+(y₂-y₁)²

Now we just plug in points from two vertices that are consecutive. By consecutive I mean next to each other (example: you can use AB, BC, CD, or AD). Let's just do AB

A: (-2,-3)

B: (4,-1)

√(x₂-x₁)²+(y₂-y₁)²

√(4-(-2))²+(-1-(-3))²

√(4+2)²+(-1+3)²

√(6)²+(2)²

√(36+4)

√(40)

Now, your teacher may want you to simplify this radical:

√(40) = √(4*10) = √(4)√(10)=2√10

I hope this explanation was thorough and answer all of your questions. If you need any additional help please don't hesitate to reach out! Learn on :)

Answer 3

Plot the points on a graph and you will see that the length of any side is √(2² + 6² ) = √40