TS EAMCET · Maths · Straight Lines
If the line \(2 x-y-4=0\) divides the line segment joining the points \((2,-1)\) and \((1,-4)\) at the point \((a, b)\) in the ratio \(m: n\) then \(4\left(a-b\left(\frac{m}{n}\right)^2\right)=\)
- A -5
- B 14
- C 11
- D 10
Answer & Solution
Correct Answer
(D) 10
Step-by-step Solution
Detailed explanation
\(\frac{m}{n} = -\frac{2(2)-(-1)-4}{2(1)-(-4)-4}\) \(\frac{m}{n} = -\frac{4+1-4}{2+4-4} = -\frac{1}{2}\) \(a = \frac{(\frac{m}{n})x_2 + x_1}{\frac{m}{n}+1} = \frac{(-\frac{1}{2})(1)+2}{-\frac{1}{2}+1} = \frac{-\frac{1}{2}+2}{\frac{1}{2}} = \frac{\frac{3}{2}}{\frac{1}{2}} = 3\)…
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