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Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of {A}{B}{C}

Question

Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of $Δ A B C$ .
(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What do you observe?
(v) If $A (x_{1}, y_{1}),$ $B (x_{2}, y_{2})$ and $C (x_{3}, y_{3})$ are the vertices of ∆ ABC, find the coordinates of the centroid of the triangle.

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Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of

Δ A B C

.
(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What do you observe?
(v) If

A (x_{1}, y_{1}),

B (x_{2}, y_{2})

and

C (x_{3}, y_{3})

are the vertices of ∆ ABC, find the coordinates of the centroid of the triangle.

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Question Text

Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of

Δ A B C

.
(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1
(iii) Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What do you observe?
(v) If

A (x_{1}, y_{1}),

B (x_{2}, y_{2})

and

C (x_{3}, y_{3})

are the vertices of ∆ ABC, find the coordinates of the centroid of the triangle.