Verified Solution • 2025–26 Session moderate

QJEEM25Ma0431: JEE Main 2025 Mathematics - Class 11 JEEM25Ma0431 Solution: Let the area of a with vertices and be 35 square units. If its…

Let the area of a △PQR\triangle P Q R with vertices P(5,4),Q(−2,4)P(5,4), Q(-2,4) and R(a,b)R(a, b) be 35 square units. If its orthocenter and centroid are O(2,145)O\left(2, \frac{14}{5}\right) and C(c,d)C(c, d) respectively, then c+2dc+2 d is equal to

Multiple Choice Options

  • A 33
  • B 73\frac{7}{3}
  • C 22
  • D 83\frac{8}{3}

Step-by-Step Verified Solution

JEE Main 2025 (Online) 23rd January Morning Shift Mathematics - Properties of Triangle Question 1 English Explanation

amp; Equation of lines QR=5x+2y+2=0amp; Equation of lines PR=10x−3y−38=0amp;∴ Point R(2,−6)amp; Centroid =(5−2+23,4+4−63)amp;=(53,23)amp;c+2d=53+43=3\begin{aligned}& \text { Equation of lines } Q R=5 x+2 y+2=0 \\& \text { Equation of lines } P R=10 x-3 y-38=0 \\& \therefore \text { Point } R(2,-6) \\& \text { Centroid }=\left(\frac{5-2+2}{3}, \frac{4+4-6}{3}\right) \\& =\left(\frac{5}{3}, \frac{2}{3}\right) \\& c+2 d=\frac{5}{3}+\frac{4}{3}=3\end{aligned}

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