Question

you are graphing rectangle abcd in the coordinate plane. the following are three of the vertices of the rectangle: a(2,1), b(5,1), and c(5,6). what are the coordinates of point d? (□,□) image of coordinate plane with rectangle abcd plotted, points a, b, c, d marked, axes labeled y and x 3 of 5 skip check

Explanation:

Step1: Recall rectangle properties

In a rectangle, opposite sides are equal and parallel, and adjacent sides are perpendicular. So, \(AB\) is parallel to \(CD\), and \(BC\) is parallel to \(AD\). Also, the \(x\)-coordinate of \(D\) should match that of \(A\), and the \(y\)-coordinate of \(D\) should match that of \(C\) (or vice versa, based on side directions).

Step2: Analyze coordinates of given points

• Point \(A\) is \((2, 1)\), point \(B\) is \((5, 1)\) (so \(AB\) is horizontal, length \(5 - 2 = 3\), \(y\)-coordinate same: \(1\)).
• Point \(B\) is \((5, 1)\), point \(C\) is \((5, 6)\) (so \(BC\) is vertical, length \(6 - 1 = 5\), \(x\)-coordinate same: \(5\)).
• For point \(D\), since \(AD\) should be vertical (parallel to \(BC\)) and \(CD\) horizontal (parallel to \(AB\)), the \(x\)-coordinate of \(D\) must be equal to the \(x\)-coordinate of \(A\) (which is \(2\)), and the \(y\)-coordinate of \(D\) must be equal to the \(y\)-coordinate of \(C\) (which is \(6\)). So \(D\) is \((2, 6)\).

Answer:

\((2, 6)\)