AP EAMCET · Maths · Straight Lines
If the axes are translated to the orthocentre of the triangle formed by the points \(\mathrm{A}(7,5), \mathrm{B}(-5,-7), \mathrm{C}(7,-7)\), then the coordinates of the incentre of the triangle in the new system are
- A \((-6,6)\)
- B \(\left(-\frac{5}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)\)
- C \(\left(\frac{-12}{2+\sqrt{2}}, \frac{12}{2+\sqrt{2}}\right)\)
- D \((-5 \sqrt{2},-7 \sqrt{2})\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{-12}{2+\sqrt{2}}, \frac{12}{2+\sqrt{2}}\right)\)
Step-by-step Solution
Detailed explanation
Vertices: \( \mathrm{A}(7,5), \mathrm{B}(-5,-7), \mathrm{C}(7,-7) \) Line AC is \( x=7 \) (vertical); Line BC is \( y=-7 \) (horizontal). Triangle ABC is right-angled at C. Orthocentre \( \mathrm{H} = \mathrm{C} = (7,-7) \) Side lengths:…
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