Lewis Cross

07/23/2023 · Escuela primaria

\begin{tabular}{l} Use the diagonals to determine whether a parallelogram with \\ vertices \( U(2,-2), V(9,-2), W(9,-6) \), and \( X(2,-6) \) is \\ a rectangle, rhombus, or square. Give all the names that apply. \\ UW \( =X V \), so \( U V W X \) is a rectangle. \\ The slope of \( \overline{U W}=-4 / 7 \) and the slope of \( \overline{X V}= \) \\ 7/4. \\ Therefore, the diagonals are perpendicular. \\ So, \( U V W X \) is a rhombus and a square. \\ \( U W=X V \), so \( U V W X \) is a rectangle. \\ The slope of \( \overline{U W}=-4 / 7 \) and the slope of \( \overline{X V}= \) \\ \( 4 / 7 \). \\ Therefore, the diagonals are not perpendicular. \\ So, \( U V W X \) is not a rhombus, nor is it a square. \\ \( U W \neq X V \), so \( U V W X \) is not a rectangle. \\ The slope of \( \overline{U W}=-4 / 7 \) and the slope of \( \overline{X V}= \) \\ \( -7 / 4 \). \\ Therefore, the diagonals are perpendicular. \\ So, \( U V W X \) is a rhombus and a square. \\ UW \( \neq X V \), so \( U V W X \) is not a rectangle. \\ The slope of \( \overline{U W}=-4 / 7 \) and the slope of \( \overline{X V}= \) \\ \( 4 / 7 \). \\ Therefore, the diagonals are not perpendicular. \\ So, \( U V W X \) is not a rhombus, nor is it a square. \\ \hline\end{tabular}