Answer:
The figure is a rectangle
Step-by-step explanation:
* Lets explain how to solve the problem
- To prove the following set of coordinates represents which figure
lets find the distance between each two points and the slopes of
the lines joining these points
- The rule of the distance between two point is
- The rule of the slope is
- <em>Remember:</em>
* Parallel lines have same slopes
* The product of the slopes of the perpendicular lines is -1
# points (7 , 10) and (4 , 7)
∵
∵
# points (4 , 7) and (6 , 5)
∵
∵
# points (6 , 5) and (9 , 8)
∵
∵
# points (9 , 8) and (7 , 10)
∵
∵
∵ d1 = d3 = √18 and d2 = d4 = √8
∴ Each two opposite sides are equal
∵ m1 = m3 = 1 and m2 = m4 = -1
∴ Each two opposite sides are parallel
∵ m1 × m2 = 1 × -1 = -1
∵ m2 × m3 = 1 × -1 = -1
∵ m3 × m4 = 1 × -1 = -1
∵ m4 × m1 = 1 × -1 = -1
∴ Each two adjacent sides are perpendicular
- The set of coordinates represents a figure has these properties:
1. Each two opposite sides are equal
2. Each two opposite sides are parallel
3. Each two adjacent sides are perpendicular
∴ The figure is a rectangle