AP EAMCET · Maths · Straight Lines
The in-centre of the triangle formed by the lines \(x=0, y=0\) and \(3 x+4 y=12\) is
- A \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
- B \((1,1)\)
- C \(\left(1, \frac{1}{2}\right)\)
- D \(\left(\frac{1}{2}, 1\right)\)
Answer & Solution
Correct Answer
(B) \((1,1)\)
Step-by-step Solution
Detailed explanation
Vertices: \(A(0,0), B(4,0), C(0,3)\) Side lengths: \(a=BC=5, b=AC=3, c=AB=4\) In-centre \((I_x, I_y) = \left(\frac{ax_A+bx_B+cx_C}{a+b+c}, \frac{ay_A+by_B+cy_C}{a+b+c}\right)\) \(I_x = \frac{5(0)+3(4)+4(0)}{5+3+4} = \frac{12}{12} = 1\)…
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