Question

use the following information to give the most precise classification for quadrilateral bear. click here for notes key. slope of ( overline{be}=\frac{1}{3} ) length of ( overline{be}=sqrt{10} ) slope of ( overline{ea}=-3 ) length of ( overline{ea}=sqrt{10} ) slope of ( overline{ar}=\frac{1}{3} ) length of ( overline{ar}=sqrt{10} ) slope of ( overline{br}=-3 ) length of ( overline{br}=sqrt{10} ) (1 point) rhombus rectangle trapezoid square

Explanation:

Step1: Check for parallel sides

Slope of \(\overline{BE}=\frac{1}{3}\) and slope of \(\overline{AR}=\frac{1}{3}\), so \(\overline{BE}\parallel\overline{AR}\).
Slope of \(\overline{EA}=- 3\) and slope of \(\overline{BR}=-3\), so \(\overline{EA}\parallel\overline{BR}\).

Step2: Check for equal - length sides

Length of \(\overline{BE}=\sqrt{10}\), length of \(\overline{EA}=\sqrt{10}\), length of \(\overline{AR}=\sqrt{10}\), length of \(\overline{BR}=\sqrt{10}\), so \(BE = EA=AR = BR\).

Step3: Check for perpendicular sides

The product of the slopes of \(\overline{BE}\) and \(\overline{EA}\) is \(\frac{1}{3}\times(-3)=- 1\), so \(\overline{BE}\perp\overline{EA}\).

Answer:

Square