Question

Given rectangle ABCD with vertices A(5,-4), B(5,4), C(-5,4) and D(-5,-4), what is the length ofthe diagonal of ABCDA 12.81B 13.54C 12.57D 25.62E11.81

Answer 1

The rectangle ABCD has coordinates given.

The diagonal is either of AC or BD, and the lengths are the same.

The distance between point A and point C (length of the diagonal) is calculated with the formula below;

`\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{The coordinates are;} \\ (x_1,y_1)=(5,-4) \\ (x_(2,)y_2)=(-5,4) \\ d=\sqrt[]{(-5-5)^2+(4-\lbrack-4\rbrack)^2} \\ d=\sqrt[]{(-10)^2+(4+4)^2} \\ d=\sqrt[]{100+(8)^2} \\ d=\sqrt[]{100+64} \\ d=\sqrt[]{164} \\ d=12.8062\ldots \\ d\approx12.81 \end{gathered}`

The correct answer is option A