JEE Main 2026 · 2 Apr · Shift 1 · Mathematics Q9

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MathematicsSingle correct+4 / -1Question 9 of 75

Let the mid points of the sides of a triangle $ABC$ be $\left(\frac52,7\right)$ , $\left(\frac52,3\right)$ and $(4,5)$ . If its incentre is $(h,k)$ , then $3h+k$ is equal to :

Answer and worked solution

Official answer: C

Vertices from midpoints. The vertices sum to the midpoints' sum $(9,15)$ ; each vertex is that sum minus twice the opposite midpoint: $(4,1)$ , $(4,9)$ , $(1,5)$ .

Sides. Opposite $(4,1)$ : 5. Opposite $(4,9)$ : 5. Opposite $(1,5)$ : 8.

Incentre.
$\frac{5(4,1)+5(4,9)+8(1,5)}{18}=\left(\frac83,5\right),\qquad3h+k=8+5=13.$

(C)

Topics:Distance and section formulae

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JEE Main 2026 · 2 Apr · Shift 1, Mathematics question 9