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Slope of a Line

A 1, 4, B 3, ...

Question

A (1, 4), B (3, 2) and C (7, 5) are vertices of a triangle ABC. Find :

(i) the co-ordinates of the centroid of triangle ABC.

(ii) the equation of a line, through the centroid and parallel to AB.

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Solution

(i) Co-ordinates of the centroid of triangle ABC are

$open parentheses fraction numerator 1 plus 3 plus 7 over denominator 3 end fraction comma fraction numerator 4 plus 2 plus 5 over denominator 3 end fraction close parentheses equals open parentheses 11 over 3 comma 11 over 3 close parentheses$

(ii) Slope of AB = $fraction numerator 2 minus 4 over denominator 3 minus 1 end fraction equals negative 1$

Slope of the line parallel to AB = Slope of AB = -1

Thus, the required equation of the line is

y - y₁ = m(x - x₁)

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