Answer :
Answer:
Firstly,
Let A(-2 3), B(6 7), C(8 3), D(0 -1) be given points of rectangle.
Step-by-step explanation:
Then, AB =
[tex] \sqrt{(6 + 2)^{2} + \sqrt{(7 - 3)^{2} } } \\ = 4 \sqrt{5} [/tex]
Now
CD=
[tex] \sqrt{(0 - 8)^{2} + ( - 1 - 3)^{2} } \\ = 4 \sqrt{5} [/tex]
Here, AB=CD
Finally,
Diagonal of AC must be equal to Diagonal of BD to prove that the given points are the vertices of a rectangle.
so,
Diagonal of AC=
[tex] \sqrt{(8 + 2)^{2} + (3 - 3) ^{2} } \\ = 10[/tex]
Diagonal of BD=
[tex] \sqrt{(0 - 6) ^{2} + ( - 1 - 7) ^{2} } \\ = 10[/tex]
Finally, Diagonal of AC = Diagonal of BD.
The given points are the vertices of Rectangle.