Laura is designing a rectangular porch for her house. on her scale drawing, the vertices of the rectangle are (2, 7), (8, 7), and (2, 9). what are the coordinates of the fourth vertex?

Coordinates of fourth vertex are (8,9)  

Step-by-step explanation:

Given that Laura is designing a rectangular porch for her house. On her scale drawing, the vertices of the rectangle are (2, 7), (8, 7), and (2, 9).

we have to find the coordinates of the fourth vertex.

As diagonals of rectangle bisect each other and are congruent then the coordinates of E is the mid-point of AC as well as BD.

By mid-point formula if (a,b) and (c,d) are the coordinates of line segment then the coordinates of mid point are

Mid-point of AC= mid point of BD

Comparing both sides , we get

and

and

and

Hence, coordinates of fourth vertex are (8,9)    

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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