Three of the four vertices of a rectangle are located at (4, 2), (7, 2) and (4, 8). a. What are the coordinates of the missing vertex? ( , ) b. Find the area and perimeter of the rectangle. Area = square units Perimeter = units

a) The coordinates of the missing vertex = (7, 8)

b) Area = 18 square units

   Perimeter = 18 units

Step-by-step explanation:

a) We know three of the four vertices:

A: (4, 2)           C ______ D(?)

B: (7, 2)               |             |

C: (4, 8)           A |______| B  

To find the coordinates of the missing vertex we need to calculate the distance in the x-direction from point A to point B:

Hence, the distance of point D from point C in the x-direction is:

Now, to find the coordinate in "y" we need to calculate the distance in the y-direction between point C and point A:

Then, the distance of point D from point B in the y-direction is:

Therefore, the coordinates of the missing vertex (point D) are:

b) The area of the rectangle is:

The perimeter is given by:

I hope it helps you!          

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0