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The Medians Ad and Be of a Triangle with Vertices a (0, B), B (0, 0) and C (A, 0) Are Perpendicular to Each Other, If - Mathematics

MCQ

The medians AD and BE of a triangle with vertices A (0, b), B (0, 0) and C (a, 0) are perpendicular to each other, if

Options

  • \[a = \frac{b}{2}\]

  • \[b = \frac{a}{2}\]

  • ab = 1

  • \[a = \pm \sqrt{2}b\]

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Solution

\[a = \pm \sqrt{2}b\]

The midpoints of BC and AC are \[D\left( \frac{a}{2}, 0 \right) \text { and } E\left( \frac{a}{2}, \frac{b}{2} \right)\]. 

Slope of AD= \[\frac{0 - b}{\frac{a}{2} - 0}\]

Slope of BE = \[\frac{- \frac{b}{2}}{\frac{- a}{2}}\]

It is given that the medians are perpendicular to each other.

\[\frac{0 - b}{\frac{a}{2} - 0} \times \frac{- \frac{b}{2}}{- \frac{a}{2}} = - 1\]

\[ \Rightarrow a = \pm \sqrt{2}b\]

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Q 29 | Page 135
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