Question

When the coordinates (2, 3), (4, 4), (6, 3), and (4, 2) are joined, which shape is formed? A. Parallelogram B. Rectangle C. Rhombus D. Square.

Answer 1

Parallelogram

Explanation:

Please refer to the attached file. Let us first see whether the opposite lines are parallel or not.

we find the slope of the lines and see if they are same for being parallel.

`slope=(y_2-y_1)/(x_2-x_1)`

we use the above formula to evaluate slopes.

Hence slope of

`AB= (4-3)/(4-6) = -(1)/(2)\\BC= (3-2)/(6-4) = (1)/(2)\\CD= (3-2)/(2-4) = -(1)/(2)\\DA= (4-3)/(4-2) = (1)/(2)`

Hence we see AB ║CD and BC║ DA

Hence it a parallelogram.

Part 2 and 4 : Check for Rectangle and square

As we see that none of the interior angle is 90° hence it is not a rectangle or a square.

Part C: Rhombus

Let us see if its diagonals are equal,

AC=4 units

BD=8 units

Hence they are not equal thus it is not a rhombus also.

There fore the figure is only a parallelogram.

Answer 2

I think the correct answer among the choices presented above is option C. When the coordinates (2, 3), (4, 4), (6, 3), and (4, 2) are joined, a rhombus is formed. This shape is a parallelogram which has opposite equal acute angles, opposite obtuse angles and four equal side lengths which can be shown by the figure of these coordinates.