A (-4,2)2, B(0,2) and C (-2,-4) Are the Vertices of a Triangle Abc. A,Q and R Are Mid-points of Sides Bc,Ca and Ab Respectively.Show that the Centroid of δ Pqr is the Same as the Centroid of δ Abc. - Mathematics

Sum

A (-4,2)2, B(0,2) and C (-2,-4) are the vertices of a triangle ABC. A,Q and R are mid-Points of sides BC,CA and AB respectively.Show that the centroid of Δ PQR is the same as the centroid of Δ ABC.

Solution

A(-4,2), B(0,2) and C(-2,-4) are the vertioes of ΔABC,

∴" Centroid of ΔABC"=((-4+0-2)/3,(2+2-4)/3)=((-6)/3,0/3)=(-2,0)

P,Q and R are the mid-points of sides BC, CA and AB respectively.

∴ "Coordinates of P"= ((0-2)/2,(2-4)/2)=(-2/2,-2/2)=(-1,1)

∴" Coordinates of Q"= ((-2-4)/2,(-4+2)/2)=((-6)/2,(-2)/2)=(-3,-1)

∴ "Coordinates of R"=((-4+0)/2, (2+2)/2)=((-4)/2,4/2)=(-2,2)

∴ "Coordinates of ΔPQR"=((-1-3-2)/3,(-1-1+2)/3)=(-6/3,0/3)=(-2,0)

⇒ Centroid of ΔABC=centroid of ΔPQR

Concept: Co-ordinates Expressed as (x,y)
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Selina Concise Maths Class 10 ICSE
Chapter 13 Section and Mid-Point Formula
Exercise 13 (C) | Q 21 | Page 183