Question

Given: The coordinates of rectangle DEFG are D(0, b), E(a, b), F(a, 0), and G(0, 0). Prove: The diagonals of a rectangle are congruent. As part of the proof, find the length of .

Answer 1

The answer to your question is below

Explanation:

Data

D (0, b)

E (a, b)

F(a, 0)

G (0, 0)

From this information, we conclude that the diagonals are EG and DF.

To prove that they are congruent we must calculate their length.

dEG =
`\sqrt{(0- b)^(2) + (0 - a)^(2)}`

dEG =
`\sqrt{b^(2) + a^(2)}`

dDF =
`\sqrt{(a - 0)^(2) + (0 - b)^(2)}`

dDF =
`\sqrt{a^(2) + b^(2)}`

Conclusion

The length of EG is equal to the length of DF, so they are congruent.