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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.

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

$\Rightarrow a = \pm \sqrt{2}b$

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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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