HPCET Centroid — practice questions

Explore 2 free Centroid questions in HPCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Centroid questions and exercises with answers

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The position vector of the **centroid** of triangle with vertices $A(\vec a),\ B(\vec b),\ C(\vec c)$ is:Read the answer and worked solution →If $G(a, 2, -1)$ is the centroid of the triangle with vertices $P(1, 3, 2),\ Q(3, b, -4),\ R(5, 1, c)$, then $(a, b, c)$ equals:Read the answer and worked solution →

Worked practice questions

The position vector of the centroid of triangle with vertices $A(\vec a),\ B(\vec b),\ C(\vec c)$ is:

$(\vec a + \vec b + \vec c)/3$
$(\vec a + \vec b + \vec c)/2$
$\vec a + \vec b + \vec c$
$(\vec a \cdot \vec b \cdot \vec c)/3$

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Correct answer: A. $(\vec a + \vec b + \vec c)/3$

Centroid $G$ divides each median internally in ratio 2:1, giving $\vec g = (\vec a + \vec b + \vec c)/3$.

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If $G(a, 2, -1)$ is the centroid of the triangle with vertices $P(1, 3, 2),\ Q(3, b, -4),\ R(5, 1, c)$, then $(a, b, c)$ equals:

$(3, 2, -1)$
$(3, -2, 1)$
$(2, 3, -1)$
$(3, 2, 1)$

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Correct answer: A. $(3, 2, -1)$

**Centroid formula:** $G = (P + Q + R)/3$. **Coordinates:** $a = (1+3+5)/3 = 3$, $2 = (3+b+1)/3$ ⇒ $b = 2$, $-1 = (2-4+c)/3$ ⇒ $c = -1$. **So $(a, b, c) = (3, 2, -1)$.**