Straight Lines

JEE Main 2025 (Online) 22nd January Morning ShiftMCQMedium📈 Topic in 21% papers+4−1

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

Let the triangle PQR be the image of the triangle with vertices (1,3),(3,1) and (2,4) in the line x+2y=2. If the centroid of is the point ( , ), then 15( - ) is equal to :

Answer

(3) 22

Solution

The image of the centroid is the centroid of the image triangle, so reflect only G.

[figure]

G= (2, 83 ); for x+2y-2=0: ax1+by1+c= 163

-21= -8/32= -2(16/3)5=- 3215

=- 215, =- 2415 15( - )=22

Answer: (3)

Keep practising — Straight Lines

Ques. 2JEE 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 .

Ques. 3JEE 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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