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QJEEM24Ma6424: JEE Main 2024 Mathematics - Class 11 JEEM24Ma6424 Solution: The equations of two sides and of a triangle are and ,…

The equations of two sides AB\mathrm{AB} and AC\mathrm{AC} of a triangle ABC\mathrm{ABC} are 4x+y=144 x+y=14 and 3x−2y=53 x-2 y=5 , respectively. The point (2,−43)\left(2,-\frac{4}{3}\right) divides the third side BC\mathrm{BC} internally in the ratio 2:12: 1 , the equation of the side BC\mathrm{BC} is

Multiple Choice Options

  • A x+6y+6=0x+6 y+6=0
  • B x−3y−6=0x-3 y-6=0
  • C x+3y+2=0x+3 y+2=0
  • D x−6y−10=0x-6 y-10=0

Step-by-Step Verified Solution

JEE Main 2024 (Online) 8th April Morning Shift Mathematics - Straight Lines and Pair of Straight Lines Question 14 English Explanation

amp;2=2x2+x13,−43=2y2+y13amp;2x2+x1=6,2y2+y1=−4\begin{aligned}& 2=\frac{2 x_2+x_1}{3}, \frac{-4}{3}=\frac{2 y_2+y_1}{3} \\& 2 x_2+x_1=6,2 y_2+y_1=-4\end{aligned}

amp;x1=6−2x2.... (1)amp;y1=−4−2y2.... (2)amp;4x1+y1=14.... (3)amp;3x2−2y2=5.... (4)\begin{aligned}& x_1=6-2 x_2 \quad \text{.... (1)}\\& y_1=-4-2 y_2 \quad \text{.... (2)}\\& 4 x_1+y_1=14 \quad \text{.... (3)}\\& 3 x_2-2 y_2=5 \quad \text{.... (4)}\end{aligned}

From here, x2=1,y2=−1,x1=4,y1=−2x_2=1, y_2=-1, x_1=4, y_1=-2

amp;B(4,−2)C(1,−1)amp;y+2=−1+21−4(x−4)amp;−3y−6=x−4amp;x+3y+2=0\begin{aligned}& B(4,-2) C(1,-1) \\& y+2=\frac{-1+2}{1-4}(x-4) \\& -3 y-6=x-4 \\& x+3 y+2=0\end{aligned}

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