The graph shows 2 sides and 3 vertices of a parallelogram.
Which point best represents the 4th vertex of the parallelogram?
A. (6, 4)
B. (7, 4)
C. (7, 5)
D. (8, 5)
C. (7, 5)
To determine which point best represents the 4th vertex of the parallelogram, we need to consider the properties of a parallelogram.
A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. In other words, the opposite sides of a parallelogram are equal in length and do not intersect.
Looking at the given information, we have 2 sides and 3 vertices of the parallelogram. Since opposite sides of a parallelogram are parallel, we can determine the direction of the missing side by finding the slope between the known sides.
Let's calculate the slope between the two known vertices to determine the direction of the missing side:
Slope = (change in y) / (change in x)
For the given points:
Point A: (x1, y1) = (6, 4)
Point B: (x2, y2) = (7, 5)
Slope_AB = (y2 - y1) / (x2 - x1)
= (5 - 4) / (7 - 6)
= 1 / 1
= 1
The slope AB is 1.
Using this information, we can find the point that best represents the 4th vertex of the parallelogram by adding the slope to the known vertex.
Since the slope of AB is 1, we can add 1 to the x-coordinate and the 4th vertex's x-coordinate will be 7.
Now we just need to find the point that has an x-coordinate of 7.
Looking at the answer choices, we can see that the point (7,5) in choice C has an x-coordinate of 7. Therefore, the point (7,5) best represents the 4th vertex of the parallelogram.
So the answer is option C. (7, 5).
To determine the best point that represents the fourth vertex of the parallelogram, we need to use the properties of a parallelogram. A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length.
Looking at the given graph, we can see that one side of the parallelogram is a vertical line connecting points (6, 2) and (6, 6). The other side of the parallelogram is a horizontal line connecting points (6, 6) and (10, 6).
To find the fourth vertex, we need to find a point that is both parallel and equal in length to the given sides. This means that the fourth vertex should be on the same vertical line as points (6, 2) and (6, 6), and on the same horizontal line as points (6, 6) and (10, 6).
Looking at the given options, the point that satisfies these conditions is (6, 4). Therefore, the correct answer is:
A. (6, 4)