Question

Jose plotted points on a coordinate plane to represent the vertices of a rectangle. The first two points are sown below. Which could be the other points Jose plotted?

Answer 1

Option C, C(5, 8) and D(1, 8), satisfies the conditions of having parallel sides and perpendicular adjacent sides, making it the correct answer.

To determine which points could be the other vertices of the rectangle based on the given information, we need to consider the properties of a rectangle.

In a rectangle, opposite sides are parallel and equal in length. Additionally, adjacent sides are perpendicular to each other.

Given that the first two points are A(2, 5) and B(2, 1), we can see that these points have the same x-coordinate (2). This means that the opposite sides of the rectangle will be vertical and parallel to the y-axis.

A. C(6, 5) and D(6, 6)

In this case, the x-coordinate of C and D is 6, which is different from the x-coordinate of A and B. This means that the opposite sides of the rectangle are not parallel. Therefore, this option is incorrect.

B. C(7, 5) and D(7, 1)

Here, the x-coordinate of C and D is 7, which is also different from the x-coordinate of A and B. Therefore, the opposite sides of the rectangle are not parallel, making this option incorrect as well.

C. C(5, 8) and D(1, 8)

In this option, the y-coordinate of C and D is 8, which is the same as the y-coordinate of A and B. This indicates that the opposite sides of the rectangle are parallel to the x-axis. Additionally, the x-coordinate of C and D are different from the x-coordinate of A and B, which means that the opposite sides are also perpendicular. Hence, this option satisfies the properties of a rectangle.

Therefore, the correct answer is C. C(5, 8) and D(1, 8) could be the other points Jose plotted to form a rectangle with points A(2, 5) and B(2, 1).

Answer 2

B. C(7,5) and D(7,1)

Step-by-step explanation

The coordinates of A are (2,5).

The coordinates of of B are (2,1).

To form a rectangle, the y-coordinates of the remaining two points should be

(a, 5) and (a,1) because A and B have the same y-coordinates.

The x-coordinates of the remaining two points should also be the same because this is a vertical line.

From the options, the best choice is

C(7,5) and D(7,1)

The correct choice is B.