Question

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

Answer 1

`"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`