COMEDK · Maths · 10. Straight Lines
The medians \(A D\) and \(B E\) of a triangle with vertices \(A(0, b), B(0,0)\) and \(C(a, 0)\) are perpendicular to each other, if
- A \(a=\frac{b}{2}\)
- B \(b=\frac{a}{2}\)
- C \(a b=1\)
- D \(a=\pm \sqrt{2} b\)
Answer & Solution
Correct Answer
(D) \(a=\pm \sqrt{2} b\)
Step-by-step Solution
Detailed explanation
We have, \(B E\) and \(A D\) are the medians. So, \(E\) and \(D\) are the mid-points of \(A C\) and \(B C\) respectively. \(\therefore\) Coordinates of \(E=\left(\frac{a}{2}, \frac{b}{2}\right)\) and coordinates of \(D=\left(\frac{a}{2}, 0\right)\) Now, slope of median…
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