To find the slopes of the sides of quadrilateral GOLD, we can use the slope formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Slope calculations for Quadrilateral GOLD:
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Slope of \( GO \) (from G to O):
- Coordinates: \( G(-1, 5) \) and \( O(2, 8) \) \[ \text{slope of } GO = \frac{8 - 5}{2 - (-1)} = \frac{3}{3} = 1 \]
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Slope of \( OL \) (from O to L):
- Coordinates: \( O(2, 8) \) and \( L(4, 4) \) \[ \text{slope of } OL = \frac{4 - 8}{4 - 2} = \frac{-4}{2} = -2 \]
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Slope of \( LD \) (from L to D):
- Coordinates: \( L(4, 4) \) and \( D(1, 1) \) \[ \text{slope of } LD = \frac{1 - 4}{1 - 4} = \frac{-3}{-3} = 1 \]
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Slope of \( GD \) (from G to D):
- Coordinates: \( G(-1, 5) \) and \( D(1, 1) \) \[ \text{slope of } GD = \frac{1 - 5}{1 - (-1)} = \frac{-4}{2} = -2 \]
Summary of Slopes:
- Slope of \( GO \) = \( 1 \)
- Slope of \( OL \) = \( -2 \)
- Slope of \( LD \) = \( 1 \)
- Slope of \( GD \) = \( -2 \)
Question 2: Is Quadrilateral QRST a parallelogram?
Without specific coordinates for the vertices of QRST, I cannot directly determine if it's a parallelogram based on slopes, but a quadrilateral is a parallelogram if:
- Opposite sides are parallel (have the same slope), or
- The midpoints of the diagonals are the same.
If you provide the coordinates for QRST, I can help determine if it is a parallelogram. If you have already determined its slopes and found that opposite sides are equal, then the answer would be "Yes." Otherwise, if they are not equal, then the answer would be "No."