Question

Is quadrilateral ABCD a square? Show your work.

Answer 1

yes

Explanation:

yes, the slope and distance from each side is equal to another

Answer 2

The answer to your question is Yes, it is a square.

Explanation:

Data

From the picture

A (8, 3)

B (7, 8)

C (2, 7)

D (3, 2)

Process

-Use the formula of the distance between two points.

-Calculate the distance between AB, BC, CD, DA

Formula

d =
`\sqrt{(x2 - x1)^(2)+ (y2 - y1)^(2)}`

1.- Distance between AB

dAB =
`\sqrt{(7 - 8)^(2)+ (8 - 3)^(2)}`

dAB =
`\sqrt{(-1)^(2)+ (5)^(2)}`

dAB =
`√(1 + 25)`

dAB =
`√(26)`

2.- Distance between BC

dBC =
`\sqrt{(2 - 7)^(2)+ (7 - 8)^(2)}`

dBC =
`\sqrt{(-5)^(2)+ (-1)^(2)}`

dBC =
`√(25 + 1)`

dBC =
`√(26)`

3.- Distance between CD

dCD =
`\sqrt{(3 - 2)^(2)+ (2 - 7)^(2)}`

dCD =
`\sqrt{(1)^(2)+ (5)^(2)}`

dCD =
`√(1 + 25)`

dCD =
`√(26)`

4.- Distance between AD

dAD =
`\sqrt{(3 - 8)^(2)+ (2 - 3)^(2)}`

dAD =
`\sqrt{(-5)^(2)+ (-1)^(2)}`

dAD =
`√(25 + 1)`

dAD =
`√(26)`

5.- Conclusion

The quadrilateral ABCD is a square because dAB = dBC = dCD = dDA