AP EAMCET · Maths · Straight Lines
The Lines \(\mathrm{L}_1: \mathrm{y}-\mathrm{x}=0\) and \(\mathrm{L}_2: 2 \mathrm{x}+\mathrm{y}=0\) intersect the line \(\mathrm{L}_3: \mathrm{y}+2=0\) at P and \(Q\) respectively. The bisector of the angle between \(L_1\) and \(L_2\) divides the line segment PQ internally at R .
Statement-I \(\quad: \quad \mathrm{PR}: \mathrm{RQ}=2 \sqrt{2}: \sqrt{5}\)
Statement-II : In any triangle, bisector of an angle divides that triangle into two similar triangles.
- A Statement-I is true, Statement-II is false
- B Statement-I is false, Statement-II is true
- C Statement-I is true, Statement-II is true, Statement-II is a correct explanation for Statement-I
- D Statement-I is true, Statement-II is true, Statement-II is not a correct explanation for Statement-I
Answer & Solution
Correct Answer
(A) Statement-I is true, Statement-II is false
Step-by-step Solution
Detailed explanation
P: \(y-x=0, y+2=0 \Rightarrow y=-2, x=-2 \Rightarrow P(-2,-2)\) Q: \(2x+y=0, y+2=0 \Rightarrow y=-2, 2x-2=0 \Rightarrow x=1 \Rightarrow Q(1,-2)\) Vertex A (intersection of \(L_1, L_2\)): \(y-x=0, 2x+y=0 \Rightarrow x=0, y=0 \Rightarrow A(0,0)\)…
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