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Gelneren [198K]
3 years ago
6

35 Points!!

Mathematics
1 answer:
nexus9112 [7]3 years ago
5 0

Answer:

- Equal midpoints of AC and BC.

- The product of the slopes of the diagonals AC and DB is -1.

Step-by-step explanation:

1. Plot the given points, as you can see in the graph attached.

2. Calculate the midpoint of AC and DB:

M_{AC}=(\frac{-5+(-1)}{2},\frac{-1+5}{2})=(-3,2)\\M_{DB}=(\frac{-9+3}{2},\frac{6+(-2)}{2})=(-3,2)

Therefore, the midpoint of AC and DB are equal.

3. Calculte the slope of the diagonals AC and DB:

m_{AC}=\frac{5-(-1)}{-1-(-5)}=\frac{3}{2}\\m_{DB}=\frac{-2-6)}{3-(-9)}=-\frac{2}{3}

4. Multiply the slopes of the diagonals:

(\frac{3}{2})(-\frac{2}{3})=-1 (AC and DB are perpendicular)

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Why is (D₁ + D₂)/2 incorrect?

This is a really helpful link:

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