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Georgia [21]
3 years ago
10

Step by step please

Mathematics
1 answer:
Nadusha1986 [10]3 years ago
3 0

Answer:

step 1.

(67-X)=180

67-180= - X

-X=-113

X=113

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Triangles abc, dbe, and fbg are all symmetric about the y-axis. what are the coordinates of the centroid?
Drupady [299]

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The coordinates of the centroid are (0, 5)

Step-by-step explanation:

The coordinates of the centroid of a triangle whose vertices (x1, y1), (x2, y2), and (x3, y3) are (\frac{x1+x2+x3}{3} , \frac{y1+y2+y3}{3})

In Δ ABC

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∴ The centroid = (\frac{-20+0+20}{3} , \frac{0+15+0}{3}) = (\frac{0}{3} , \frac{15}{3}) = (0, 5)

∴ The coordinates of the centroid of Δ ABC are (0, 5)

In Δ DBE

∵ D = (-15, 0), B = (0, 15), E = (15, 0)

∴ x1 = -15, x2 = 0, x3 = 15

∴ y1 = 0, y2 = 15, y3 = 0

∴ The centroid = (\frac{-15+0+15}{3} , \frac{0+15+0}{3}) = (\frac{0}{3} , \frac{15}{3}) = (0, 5)

∴ The coordinates of the centroid of Δ DBE are (0, 5)

In Δ FBG

∵ F = (-5, 0), B = (0, 15), G = (5, 0)

∴ x1 = -5, x2 = 0, x3 = 5

∴ y1 = 0, y2 = 15, y3 = 0

∴ The centroid = (\frac{-5+0+5}{3} , \frac{0+15+0}{3}) = (\frac{0}{3} , \frac{15}{3}) = (0, 5)

∴ The coordinates of the centroid of Δ FBG are (0, 5)

∵ The three triangles are symmetric about the y-axis

→ That means they have the same centroid and it lies on the y-axis

∴ The coordinates of the centroid are (0, 5)

8 0
2 years ago
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