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

The answer to your question is 10 units

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 =
`√(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