Answer:
Explanation:
To determine if each pair of sides in quadrilateral RSTU are parallel or perpendicular, we can analyze the slopes of the sides.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slopes of the sides:
1. Side RS:
- Coordinates: R(0,0), S(6,3)
- Slope = (3 - 0) / (6 - 0) = 3/6 = 1/2
2. Side ST:
- Coordinates: S(6,3), T(5,5)
- Slope = (5 - 3) / (5 - 6) = 2/-1 = -2
3. Side TU:
- Coordinates: T(5,5), U(-1,2)
- Slope = (2 - 5) / (-1 - 5) = -3/-6 = 1/2
4. Side UR:
- Coordinates: U(-1,2), R(0,0)
- Slope = (0 - 2) / (0 - (-1)) = -2/1 = -2
Now, let's analyze the slopes:
- The slopes of RS and TU are equal (1/2), so these sides are parallel.
- The slopes of ST and UR are also equal (-2), so these sides are parallel.
Based on the slopes, we can conclude that RS is parallel to TU, and ST is parallel to UR.
To determine if any pair of sides are perpendicular, we need to check if the product of their slopes is -1.
- The product of the slopes of RS and ST is (1/2) * (-2) = -1, so these sides are perpendicular.
In summary, in quadrilateral RSTU:
- RS is parallel to TU
- ST is parallel to UR
- RS is perpendicular to ST