1. Find the centroid of the system consisting of a mass of 1 at (-9, 4), a mass

Question

1. Find the centroid of the system consisting of a mass of 1 at (-9, 4), a mass of 9 at (-5, -3), and a mass of 5 at (-3, -4). You may enter your answer either as a decimal or a fraction. If you use decimal form, it must be accurate to within 0.001.
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2. Find the centroid of the system consisting of a mass of 4 at (7, -2), a mass of 7 at (5, -7), a mass of 1 at (6, -9), and a mass of 7 at (-8, 0). You may enter your answer either as a decimal or a fraction. If you use decimal form, it must be accurate to within 0.001.
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3. Find the centroid of the region bounded by x + y = 1, x + 2y = -8, x = -2, and x = 4. You should enter the coordinates of your answer either as decimals or fractions. Your answer must be accurate to within 0.001.
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4. Find the centroid of the region bounded by 7x + 4y = -8, 3x ? 4y = 8, and x = -4. You should enter the coordinates of your answer either as decimals or fractions. Your answer must be accurate to within 0.001.
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Explanation / Answer

1) Centroid

X coordinate = ((1 * -9) + (9 * -5) + (5 * -3))/(1 + 9 + 5) = -4.6

Y coordinate = ((1 * 4) + (9 * -3) + (5 * -4))/(1 + 9 + 5) = -2.867

Hence centeroid = (-4.6, -2.867)

2) Similarly Solve for this case:

Answer X coordinate = ((4 * 7) + (7*5) + (1*6) + (7*-8))/(4 + 7 + 1 + 7) = 0.6842

Y coordinate = ((4 * -2) + (7*-7) + (1*-9) + (7*0))/(4 + 7 + 1 + 7) = -3.474

Centroid = (0.6842, -3.474)

3) Solving the systems of equation we get:

Points as: (-2,3), (-2,-3), (4,-3), (4,-6)

Hence centroid = (-2 - 3 + 4 + 4)/4 , (3 - 3 - 3 - 6)/4 = (0.75, -2.25)

4) Similarly here:

Points of intersection

(-4, 5); (-4, -5); (0, -2)

Hence centroid = Xcoordinate = (-4 - 4 + 0)/3 = -8/3 = -2.667

Y coordinate = -2/3 = -0.667

Hence centroid = (-2.667, -0.667)

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