Question

A house with a rectangle base is built on a plot of land. The southwest corner of the plot is designated with coordinates (0,0). The corners of the house are located at the points with coordinates (20,20), (5,40), (33,61), and (48,41), where distances are measured in feet. What are the length and width of the base of the house?

Answer 1

The width of the base of the house is 25 feet

The length of the base of the house is 35 feet

Explanation:

Displayed in the attachment is the plot of land drawn out in WXYZ(not to scale)

With the southwest corner coordinate (0,0) as the reference point

Plotted out is the base of the house built on it with coordinates (20,20),(5,40),(33,61),(48,41)

With A and B labelled width and length respectively

Length between coordinates is given as

Length=√(〖(x2-x1)〗^2+(〖y2-y1)〗^2 )

To find the width A,the points with coordinates (20,20) and (5,40) are used or (33,61) and (48,41)

Using point with coordinates (20,20) and (5,40)

Width, A=√(〖(5-20)〗^2+(〖40-20)〗^2 )=35

with x1=20, y1=20, x2=5, y2=40

Also try using points with coordinates (33,61) and (48,41).You will get same answer(opposite sides of a rectangle are equal)

To find the length B,the points with coordinates (48,41) and (20,20) are used or (5,40) and (33,61)

Using point with coordinates (48,41) and (20,20)

Length,B=√(〖(48-20)〗^2+(〖41-20)〗^2 )=25

with x1=20, y1=20, x2=48, y2=41

Also try using points with coordinates (5,40) and (33,61).You will get same answer(opposite sides of a rectangle are equal)