Straight Lines

JEE Main 2025 (Online) 23rd January Morning ShiftMCQMedium📈 Topic in 32% papers+4−1

Ques. 1JEE Main 2025, 23 January (Morning Shift)

Let the area of a PQR with vertices P(5,4), Q(-2,4) and R(a,b) be 35 square units. If its orthocenter and centroid are O (2, 145 ) and C(c,d) respectively, then c+2d is equal to

Answer

(1) 3

Solution

PQ is horizontal with PQ=7: 12 7 |b-4|=35 |b-4|=10

Altitude from R is vertical and passes through O (2, 145 ) a=2

[figure]

PO QR: slope PO= 25 slope QR=- 52= b-44 b=-6, so R(2,-6)

Centroid C= ( 5-2+23, 4+4-63 )= ( 53, 23 ) c+2d=3

Answer: (1)

Keep practising — Straight Lines

Ques. 2JEE Main 2025, 23 January (Evening Shift)

A rod of length eight units moves such that its ends A and B always lie on the lines x-y+2=0 and y+2=0, respectively. If the locus of the point P, that divides the rod AB internally in the ratio 2:1 is 9 (x2+ y2+ xy+ x+28y )-76=0, then - - is equal to :

Ques. 3JEE 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 :

Ques. 4JEE 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. 5JEE 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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