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

B. What are the dimensions of the rectangle?

C. What is the area of the rectangle?

(a) (-4,1)

(b) 3 units by 6 units

(c)18 square units

Step-by-step explanation:

Let the rectangle be ABCD labeled from the top left clockwise.

(a)Considering the y coordinates of BC,

The distance between BC =|4-1|=3 Units

Since BC and AD are congruent

Distance between A(-4,4) and D(-4,y) is also 3 Units

Therefore:

|4-y|=3

y=4-3=1

The coordinates of the fourth vertex of the rectangle at D is (-4,1)

(b)

Height, BC =3 Units

Now, A(-4,4) and B(2,4)

Therefore: Width, AB = |2-(-4)|=2+4=

Width, AB=6 Units

The dimensions of the rectangle are 3 units by 6 units.

(c)

Area of the Rectangle =Width X Height

= 3 X 6

=18 Square units

42.4

step-by-step explanation:

convert to decimal