Start by plotting and connecting the vertices to create a quadrilateral.

The figure that is created has 4 right angles and sides of equal length. The only answer choice that shares these characteristics is the square.

Once Points A,B, and C have been plotted the missing coordinates in order to form a square (all sides being equal), Point D would be (2,7). All coordinates (x,y) in Quadrant one will be positive integers.

Another approach is to calculate the distance between each point.

When Point A and Point B are plotted they form a horizontal line that goes from 2 to 7. That makes the distance .

When Point B and Point C are plotted they form a vertical line that goes from 2 to 7. That makes the distance .

Point C creates a vertical line with Point B.  That makes the distance .

From here, we want to find a point that is horizontally 5 units from Point C and vertically 5 units from Point A. Thus (2,7) is the correct answer.

Each of the points is written as an ordered pair.  The first number in each ordered pair shows where the point is located on the x-axis.  The second number in each ordered pair shows where the point is located on the y-axis.  If you plot the ordered pairs listed in the problem, the ordered pair that is needed to complete the points of a square is .

From the origin is to the right 5 and down 6 making it in quadrant IV.

Begin at point (0, 0) in the bottom left hand corner of the coordinate plane. From there, count the number of spaces you move to the right to line up with Point B. This will be the first number in the ordered pair. Next, count the number of spaces to move up until you reach Point B. This will be the second number in your ordered pair.  

You should have counted 2 spaces to the right and 8 spaces up. The ordered pair for Point B is (2, 8).

Begin at point (0, 0) in the bottom left hand corner of the coordinate plane. From there, count the number of spaces you move to the right to line up with Point A. This will be the first number in the ordered pair. Next, count the number of spaces to move up until you reach Point A. This will be the second number in your ordered pair.  

Start at point (0, 0) in the bottom, left corner of the the coordinate plane. From there, count right 6 spaces. This is the first number in the given ordered pair. From that point, count up 7 spaces. This is the second number in the given ordered pair.

By moving right 6 and up 7, you should have found Point C.

Start at point (0, 0) in the bottom, left corner of the the coordinate plane. From there, count right 2 spaces. This is the first number in the given ordered pair. From that point, count up 8 spaces. This is the second number in the given ordered pair.

Begin by plotting the points and connecting the vertices.

The quadrilateral that is created has two sets of parallel sides. Out of the possible answer choices, this can describe both squares and parallelograms. Because the figure does not contain right angles and the sides are not all the same length, it must be a parallelogram.

Begin by plotting and connecting the vertices.

The quadrilateral that is created has two sets of parallel sides. Out of the possible answer choices, this can describe both rhombuses and parallelograms. Because the sides are not all the same length, it must be a parallelogram.