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In the diagram overline (BD) is a diameter of circle A. If the slope of overleftrightarrow (BE) is (3)/(2) what is the slope of overleftrightarrow (BD) A. (3)/(2) B. -(3)/(2) C. (2)/(3) D. -(2)/(3)

Question

In the diagram
overline (BD) is a diameter of circle A. If the slope of
overleftrightarrow (BE)
is (3)/(2) what is the slope of
overleftrightarrow (BD)
A. (3)/(2)
B. -(3)/(2)
C. (2)/(3)
D. -(2)/(3)

In the diagram overline (BD) is a diameter of circle A. If the slope of overleftrightarrow (BE) is (3)/(2) what is the slope of overleftrightarrow (BD) A. (3)/(2) B. -(3)/(2) C. (2)/(3) D. -(2)/(3)

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SableElite · Tutor for 8 years

Answer

To find the slope of line \(\overleftrightarrow{BD}\), we need to use the fact that \(AD\) is the diameter of the circle and \(\overrightarrow{BD}\) is also a diameter as given in the question. Since \(AD\) and \(BD\) are both diameters of the same circle and share the endpoint \(D\), they must coincide and thus are the same line.Now, we know that \(\overleftrightarrow{BE}\) intersects the diameter \(\overleftrightarrow{AD}\) (which is the same as \(\overleftrightarrow{BD}\)) at point \(B\). Since \(\overleftrightarrow{BE}\) has a slope of \(\frac{3}{2}\), the line perpendicular to it (which would be the diameter \(\overleftrightarrow{BD}\)) will have a slope that is the negative reciprocal of \(\frac{3}{2}\).The negative reciprocal of \(\frac{3}{2}\) is calculated by flipping the fraction and changing the sign, which gives us \(-\frac{2}{3}\).Therefore, the slope of \(\overleftrightarrow{BD}\) is \(-\frac{2}{3}\).The final answer is:D. \(-\frac{2}{3}\)
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