One side of a parallelogram has endpoints (3, 3) and (1, 7).
What are the endpoints for the side opposite?
(8, 1) and (6, 7)
(6, 1) and (2, 3)
(6, 1) and (8, 5)
(8, 1) and (6, 5)
look at the change in x and y
x changes by -2, y changes by +4
the only choice that does the same is
(8, 1) and (6, 5)
To find the endpoints for the side opposite to the given side of the parallelogram, we need to use the properties of a parallelogram.
In a parallelogram, opposite sides are equal in length and parallel to each other. So, we can find the slope of the given side and extend it to find the endpoints for the side opposite.
Let's calculate the slope of the given side:
slope = (y2 - y1) / (x2 - x1)
Given points: (3, 3) and (1, 7)
Slope = (7 - 3) / (1 - 3)
Slope = 4 / -2
Slope = -2
Now, we have the slope of the given side. We can use this slope to find the new points for the side opposite.
Considering the given options:
(8, 1) and (6, 7):
The slope of this line is (7 - 1) / (6 - 8) = 6 / -2 = -3, which does not match the slope of the given side (-2). So, these points are not the endpoints for the side opposite.
(6, 1) and (2, 3):
The slope of this line is (3 - 1) / (2 - 6) = 2 / -4 = -0.5, which does not match the slope of the given side (-2). So, these points are not the endpoints for the side opposite.
(6, 1) and (8, 5):
The slope of this line is (5 - 1) / (8 - 6) = 4 / 2 = 2, which does not match the slope of the given side (-2). So, these points are not the endpoints for the side opposite.
(8, 1) and (6, 5):
The slope of this line is (5 - 1) / (6 - 8) = 4 / -2 = -2, which matches the slope of the given side (-2). So, these points are the endpoints for the side opposite.
Therefore, the correct answer is (8, 1) and (6, 5).