Q2 of 112 Page 146

Find the centroid of the triangle whose vertices are

(i) (1,3), (2, 7) and (12, – 16)


(ii) (3, – 5), (–7, 4) and (10, – 2)

i). The centroid G (x, y) of a triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3) is given by:


G (x, y) =


We have (x1, y1) = (1,3), (x2, y2) = (2, 7) and (x3, y3) = (12, – 16)


G (x, y) =


=


= (5, –2)


ii). The centroid G (x, y) of a triangle whose vertices are (x1, y1), (x2, y2) and (x3, y3) is given by:


G (x, y) =


We have (x1, y1) = (3, –5), (x2, y2) = (–7, 4) and (x3, y3) = (10, –2)


G (x, y) =


=


= (2, –1)


More from this chapter

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1

Find the midpoint of the line segment joining the points

(i) (1, – 1) and (–5, 3) (ii) (0,0) and (0,4)

 3

The center of a circle is at (–6, 4). If one end of a diameter of the circle is at the origin, then find the other end.

 4

If the centroid of a triangle is at (1, 3) and two of its vertices are (–7, 6) and (8, 5) then find the third vertex of the triangle.

 5

Using the section formula, show that the points A (1,0), B (5,3), C (2,7) and D (–2, 4) are the vertices of a parallelogram taken in order.