XYZ and ABC are similar triangles. Given the dimensions shown in the diagram, what is the area of triangle ABC ? Express the ans
wer in square units.
1 answer:
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Answer:
= 8
= 6
Therefore the co-ordinate of the center of mass is =
Step-by-step explanation:
Center of mass: Center of mass of an object is a point on the object. Center of mass is the average position of the system.
Center of mass of a triangle is the centriod of a triangle.
Given that m₁= 4, m₂=3, m₃=3 and the points are P₁(2,-3), P₂(-3,1) and P₃(3,5)
= ∑(mass × x-co-ordinate)
= ∑(mass × y-co-ordinate)
Therefore
= (4×2)+{3×(-3)}+(3×3)
=8
= {4×(-3)}+{3×1}+(3×5)
=6
The x co-ordinate of the center of mass is the ratio of to the total mass.
The y co-ordinate of the center of mass is the ratio of to the total mass.
Total mass (m) = m₁+ m₂+ m₃
= 4+3+3
=10
The x co-ordinate of the center of mass is
The y co-ordinate of the center of mass is
Therefore the co-ordinate of the center of mass is =