If area of the triangle formed by the points (1,−2),(3,4) and (2,0) is half of the area of triangle formed by the points (3,4),(2,0) and (α,α2), then distance between centroids of respective triangles is
A
√353 units
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B
2 units
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C
√373 units
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D
√393 units
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Solution
The correct option is C√373 units 12∣∣∣1321−240−2∣∣∣=14∣∣∣3α234α204∣∣∣⇒4=|α2−4α+8|⇒α2−4α+8=4(∵α2−4α+8=(α−2)2+4>0) ⇒α2−4α+4=0 (α−2)2=0
∴α=2
∴ centroid of triangle with coordinates (1,−2),(3,4) and (2,0) is G1=(2,23)
Centroid of triangle with coordinates (3,4),(2,0) and (2,4) is G2=(73,83) ∴G1G2=√(2−73)2+(63)2=√19+369=√373