Mathematics · 2025
JEE Main · 4 April 2025, Shift 1 · Q10
Let the three sides of a triangle are on the lines 4 x-7 y+10=0, x+y=5 and 7 x+4 y=15. Then the distance of its orthocentre from the orthocentre of…
Let the three sides of a triangle are on the lines $\displaystyle 4 x-7 y+10=0, x+y=5$ and $\displaystyle 7 x+4 y=15$. Then the distance of its orthocentre from the orthocentre of the tringle formed by the lines $\displaystyle x=0, y=0$ and $\displaystyle x+y=1$ is
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle \sqrt{5}$
More from Straight Lines
- Consider the lines x(3 λ+1)+y(7 λ+2)=17 λ+5, λ being a parameter, all passing through a point P. One of these lines (say L ) is farthest from the…2025
- Let ABC be a triangle formed by the lines 7 x-6 y+3=0, x+2 y-31=0 and 9 x-2 y-19=0. Let the point (h, k) be the image of the centroid of Δ ABC in the…2025
- Let the vertex A of a triangle A B C be (1,2), and the mid-point of the side A B be (5,-1). If the centroid of this triangle is (3,4) and its…2026
- Let A(6,8), B(10 cos α,-10 sin α) and C(-10 sin α, 10 cos α), be the vertices of a triangle. If L(a, 9) and G(h, k) be its orthocenter and centroid…2025
- Let the area of the triangle formed by a straight line L: x+b y+c=0 with co-ordinate axes be 48 square units. If the perpendicular drawn from the…2025
- 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,…2025
- In an equilateral triangle P Q R, let the vertex P be at (3,5) and the side Q R be along the line x+y=4. If the orthocentre of the triangle PQR is…2026
- Let A(1,0), B(2,-1) and C(7/3, 4/3) be three points. If the equation of the bisector of the angle ABC is α x+β y=5, then the value of α^2+β^2 is2026
JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.