Question

ABC is a triangle and G(4,3) is the centroid of the triangle. If A = (1, 3), B = (4, b) and C = (a, 1), find 'a' and 'b'. Find the length of side BC.
[4 MARKS]

Answer 1

Formula: 1 Mark
Value of 'a' and 'b': 1 Mark each
Length of BC: 1 Mark

For the centroid of a triangle, we have:
$x=\frac{x_1+x_2+x_3}{3}$ and $y=\frac{y_1+y_2+y_3}{3}$
$\Rightarrow 4=\frac{1+4+a}{3}$ and $3=\frac{3+b+1}{3}$
$\Rightarrow 12-5=a$ and $9-4=b$
$\Rightarrow a=7$ and $b=5$
BC $=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
Now, $=\sqrt{(7-4{)}^2+(1-5{)}^2}=\sqrt{3^2+4^2}$
$=\sqrt{9+16}=\sqrt{25}=5$
$\therefore$ The length of BC is 5 units.