Question

Four points are drawn on the coordinate plane and connected with straight lines to form a rectangle. Three of the vertices of the rectangle are located at (2, 1), (2, 4), and (-4, 4). What are the coordinates of the fourth vertex of the rectangle? What are the dimensions of the rectangle? What is the area of the rectangle?

Answer 1

Length is 4 - 1 = 3

Width is 2+4

Length times width is going to get you 18 which is your final answer

Answer 2

To find the fourth vertex of the rectangle, we can start by drawing a diagram:

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|

| (2,4)

|

--------.--------

|

(?, ?) | (2,1)

|

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We know that opposite sides of a rectangle are parallel, so the fourth vertex must be located on the same horizontal line as the point (2, 1) and the same vertical line as the point (-4, 4). Therefore, the fourth vertex must be located at (-4, 1).

To find the dimensions of the rectangle, we can find the distance between the points (2, 1) and (2, 4) to get the length of one side, and the distance between the points (2, 1) and (-4, 1) to get the length of the other side.

Length = 4 - 1 = 3

Width = 2 - (-4) = 6

So the dimensions of the rectangle are 6 by 3.

To find the area of the rectangle, we can multiply the length and width together:

Area = Length x Width = 6 x 3 = 18 square units.