1 answer

What is the area of a rectangle with vertices at #(2,3), (7,3), (7,10),# and #(2,10)#?

Question:

What is the area of a rectangle with vertices at #(2,3), (7,3), (7,10),# and #(2,10)#?

Answers

# 35" sq. unit"#.

Explanation:

Let us name the given points as

#A(2,3), B(7,3), C(7,10) and D(2,10)#.

Using the distance formula, we have,

#AB^2=(2-7)^2+(3-3)^2=25,#

#BC^2=(7-7)^2+(3-10)^2=49#,

#CD^2=(7-2)^2+(10-10)^2=25#, and,

#DA^2=(2-2)^2+(10-3)^2=49#.

Also, #AC^2=(2-7)^2+(3-10)^2=25+49#, showing that,

#AC^2=AB^2+BC^2#.

We conclude that #ABCD# is, indeed, a rectangle, having sides

#AB=5, BC=7#.

Hence, the reqd. area#=5xx7=35" sq. unit"#.

.

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