Question

Is quadrilateral ABCD a square? Show your work.

Answer 1

Answer:

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

Step-by-step 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 = $\sqrt{1 + 25}$

dAB = $\sqrt{26}$

2.- Distance between BC

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

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

dBC = $\sqrt{25 + 1}$

dBC = $\sqrt{26}$

3.- Distance between CD

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

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

dCD = $\sqrt{1 + 25}$

dCD = $\sqrt{26}$

4.- Distance between AD

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

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

dAD = $\sqrt{25 + 1}$

dAD = $\sqrt{26}$

5.- Conclusion

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

Answer 2

Answer:

yes

Step-by-step explanation:

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