Question

19 consider figure abcd, a rectangle graphed on the coordinate plane. if the slope of side (overline{bc}) is (\frac{2}{3}), what is the slope of side (overline{cd})? a (\frac{2}{3}) b (-1) c (-\frac{3}{2}) d (90^{circ})

Explanation:

Step1: Recall property of rectangle sides

In a rectangle, adjacent sides are perpendicular.

Step2: Recall slope relation of perpendicular lines

If the slope of one line is \(m_1\) and the slope of a perpendicular line is \(m_2\), then \(m_1\times m_2=- 1\). Given \(m_1 = \frac{2}{3}\), let \(m_2\) be the slope of \(\overline{CD}\). So \(\frac{2}{3}\times m_2=-1\).

Step3: Solve for \(m_2\)

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Answer:

C. \(-\frac{3}{2}\)