First slide

Cartesian plane

Question

In $ΔABC,$ the coordinates of B are (0,0) $AB = 2, ∠ ABC = \frac{π}{3}$ , and the middle point of BC has coordinates (2,0) the centroid of the triangle is

Moderate

A

(1) $(1 / 2, \sqrt{3} / 2)$
B

(2) $(5 / 3, 1 / \sqrt{3})$
C

$(4 + \sqrt{3} / 3, 1 / 3)$
D

none of these

Solution

(2,0) is the midpoint of B(0,0) and C. Then C has coordinates (4,0). Also, A has coordinates $(0 + 2 cosπ / 3, 0 + 2 sinπ / 3) \equiv (1, \sqrt{3}) .$ Then the centroid is $(5 / 3, 1 / \sqrt{3})$

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