AP EAMCET · Maths · Straight Lines
If the coordinates of the vertices of a \(\triangle A B C\) are \(A(7,6,4), B(5,4,6), C(3,2,0)\) and the bisector of \(\angle B A C\) meets the side \(B C\) at \(D\), then the coordinates of \(D\) are
- A \(\left(\frac{13}{3}, \frac{10}{3}, 4\right)\)
- B \(\left(\frac{11}{3}, \frac{8}{3}, 2\right)\)
- C \((9,8,6)\)
- D \((7,5,3)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{13}{3}, \frac{10}{3}, 4\right)\)
Step-by-step Solution
Detailed explanation
\(\because A D\) is the angle bisector of \(\angle A\). \(\Rightarrow \quad \frac{A B}{A C}=\frac{B D}{C D}\) Now, \(\begin{aligned} & A B=\sqrt{4+4+4}=2 \sqrt{3} \\ & A C=\sqrt{16+16+16}=4 \sqrt{3}\end{aligned}\)…
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