Question

Point upper A has coordinates left parenthesis negative 3 comma negative 1 right parenthesis. Point upper B has coordinates left parenthesis 1 comma 5 right parenthesis. Point upper C has coordinates left parenthesis 4 comma 3 right parenthesis. Point upper D has coordinates left parenthesis 0 comma negative 3 right parenthesis.


Determine the coordinates of the rectangle, then compute the area.

(1 point)
Responses

22 units2
22

units
2

22 units squared

26 units2
26

units
2

26 units squared

11 units2
11

units
2

11 units squared

52 units2

Answer 1

The four points are the rectangle's vertices: A(-3,-1), B(1,5), C(4,3), D(0,-3).

AB = (4,6) and BC = (3,-2). AB · BC = 4·3 + 6·(−2) = 12 − 12 = 0, so adjacent sides are perpendicular.
|AB| = sqrt(4^2+6^2)=sqrt52, |BC| = sqrt(3^2+(-2)^2)=sqrt13, so area = |AB|·|BC| = sqrt52·sqrt13 = sqrt676 = 26.

Area = 26 square units.