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प्रश्न
A(3, 1), B(y, 4) and C(1, x) are vertices of triangle ABC and G(3, 4) is its centroid. Find the values of x and y. Also, find the length of side BC.
बेरीज
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उत्तर
Since, G(4, 3) is the centroid of ΔABC, we have
`(3 + y + 1)/3 = 3` and `(1 + 4 + x)/3 = 4`
`=>` 4 + y = 9 and 5 + x = 12
`=>` y = 5 and x = 7
Hence, the values of x and y are x = 7 and y = 5.
The coordinates of the point B and C are (5, 4) and (1, 7) respectively.
Length of side BC = `sqrt((1 - 5)^2 + (7 - 4)^2`
= `sqrt((-4)^2 + (3)^2`
= `sqrt(16 + 9)`
= `sqrt(25)`
= 5 units
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