To determine which four-sided figure has two sides with negative slopes, we need to examine the slopes of the sides formed by the endpoints of each figure provided. A side has a negative slope if it goes downwards as you move from left to right.
Let's analyze each set of points:
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(–4, –4), (–4, –1), (–1, –4), (–1, –1)
- From (–4, –4) to (–4, –1): This side is vertical (slope is undefined).
- From (–4, –1) to (–1, –1): This side is horizontal (slope = 0).
- From (–1, –1) to (–1, –4): This side is vertical (slope is undefined).
- From (–1, –4) to (–4, –4): This side is horizontal (slope = 0).
No negative slopes.
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(–2, –4), (–1, –1), (1, –1), (2, –4)
- From (–2, –4) to (–1, –1): \[ \text{slope} = \frac{-1 - (-4)}{-1 - (-2)} = \frac{3}{1} = 3 \quad (\text{positive slope}) \]
- From (–1, –1) to (1, –1): This side is horizontal (slope = 0).
- From (1, –1) to (2, –4): \[ \text{slope} = \frac{-4 - (-1)}{2 - 1} = \frac{-3}{1} = -3 \quad (\text{negative slope}) \]
- From (2, –4) to (–2, –4): This side is horizontal (slope = 0).
One negative slope.
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(1, 1), (2, 4), (5, 4), (4, 1)
- From (1, 1) to (2, 4): \[ \text{slope} = \frac{4 - 1}{2 - 1} = \frac{3}{1} = 3 \quad (\text{positive slope}) \]
- From (2, 4) to (5, 4): This side is horizontal (slope = 0).
- From (5, 4) to (4, 1): \[ \text{slope} = \frac{1 - 4}{4 - 5} = \frac{-3}{-1} = 3 \quad (\text{positive slope}) \]
- From (4, 1) to (1, 1): This side is horizontal (slope = 0).
No negative slopes.
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(1, 4), (2, 1), (5, 1), (4, 4)
- From (1, 4) to (2, 1): \[ \text{slope} = \frac{1 - 4}{2 - 1} = \frac{-3}{1} = -3 \quad (\text{negative slope}) \]
- From (2, 1) to (5, 1): This side is horizontal (slope = 0).
- From (5, 1) to (4, 4): \[ \text{slope} = \frac{4 - 1}{4 - 5} = \frac{3}{-1} = -3 \quad (\text{negative slope}) \]
- From (4, 4) to (1, 4): This side is horizontal (slope = 0).
Two negative slopes.
Thus, the four-sided figure that has two sides with negative slopes is: (1, 4), (2, 1), (5, 1), (4, 4).
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