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प्रश्न
A(5, x), B(−4, 3) and C(y, –2) are the vertices of the triangle ABC whose centroid is the origin. Calculate the values of x and y.
उत्तर
Co-ordinates of centroid of ΔABC are (0, 0)
∴ `0 = (x_1 + x_2 + x_3)/3`
= `(5 - 4 + y)/3`
`=> 0 = (y + 1)/3`
`=>` y + 1 = 0
∴ y = –1
Again `0 = (y_1 + y_2 + y_3)/3`
= `(x + 3 - 2)/3`
`=> 0 = (x + 1)/3`
`=>` x + 1 = 0
∴ x = –1
∴ x = –1, y = –1
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संबंधित प्रश्न
The co-ordinates of the centroid of a triangle PQR are (2, –5). If Q = (–6, 5) and R = (11, 8); calculate the co-ordinates of vertex P.
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Point P is the midpoint of seg AB. If co-ordinates of A and B are (-4, 2) and (6, 2) respectively then find the co-ordinates of point P.
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From the figure given alongside, find the length of the median AD of triangle ABC. Complete the activity.
Solution:
Here A(–1, 1), B(5, – 3), C(3, 5) and suppose D(x, y) are coordinates of point D.
Using midpoint formula,
x = `(5 + 3)/2`
∴ x = `square`
y = `(-3 + 5)/2`
∴ y = `square`
Using distance formula,
∴ AD = `sqrt((4 - square)^2 + (1 - 1)^2`
∴ AD = `sqrt((square)^2 + (0)^2`
∴ AD = `sqrt(square)`
∴ The length of median AD = `square`
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