Question

The points (-3,-1) and (-3,5) are adjacent vertices of a rectangle. Two of the sides of the rectangle have a length of 8 units. What is the length of a diagonal of the rectangle?

Answer 1

Answer:

The answer to your question is 10 units

Step-by-step explanation:

Data

A (-3, -1)

B (-3 , 5)

length of a side = 8 units

Process

1.- Calculate the distance between A and B

dAB = $\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}$

x1 = -3     y1 = -1

x2 = -3    y2 = 5

-Substitution

dAB = $\sqrt{(-3 + 3)^{2}+ (5 + 1)^{2}}$

dAB = $\sqrt{0^{2} + 6^{2}}$

dAB = $\sqrt{36}$

dAB = 6 u

2.- Calculate the diagonal using the Pythagorean theorem.

    c² = a² + b²

    c² = 6² + 8²

    c² = 36 + 64

    c² = 100

    c = 10 units

- Conclusion

The diagonal of the rectangle measures 10 units