What is the area of the parallelogram with the given vertices? A(-1, 3), B(0, 4), C(2, 2), D(1, 1)

1 Answer
Alan P. · Stefan V.
Jan 8, 2016

#"Area"_("ABCD")=4#

Explanation:

#"Slope"_("AB") = (4-3)/(0-(-1)) = 1#

#"Slope"_("AD")=(1-3)/(1-(-1))= -1#

Since

#color(white)("XXX")"Slope"_text(AB) = - 1/("Slope"_text(AD))#

#AB# and #AD# are perpendicular and the parallelogram is a rectangle.

Therefore

#color(white)("X")"Area"_("ABCD") = |AB| xx |AD|#

#color(white)("XXXXXXX")=sqrt((4-3)^2+(0-(-1))^2)xxsqrt((1-3)^2+(1-(-1))^2)#

#color(white)("XXXXXXX")=sqrt(2)xx2sqrt(2)#

#color(white)("XXXXXXX")=4#

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