Straight Lines

JEE Main 2025 (Online) 22nd January Evening ShiftNumericalMedium📈 Topic in 32% papers+4

Ques. 1JEE Main 2025, 22 January (Evening Shift)

Let A(6,8), B(10 ,-10 ) and C(-10 ,10 ), be the vertices of a triangle. If L(a,9) and G(h,k) be its orthocenter and centroid respectively, then (5a-3h+6k+100 2 ) is equal to .

Answer

145

Solution

OA=OB=OC=10 circumcentre is O, so orthocentre L=A+B+C and centroid G= L3

[figure]

y: 9=8+10( - ) 10( - )=1, a=6+1=7; squaring: 100 2 =99

G= ( 73,3 ) 5a-3h+6k+100 2 =35-7+18+99=145

Answer: 145

Keep practising — Straight Lines

Ques. 2JEE Main 2025, 22 January (Evening Shift)

Let the distance between two parallel lines be 5 units and a point P lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the parallel lines, while R lies on the other. Then (QR)2 is equal to .

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