Question

A rectangle is drawn on a coordinate plane with vertices (0,0)
(
0
,
0
)
, (2,2)
(
2
,
2
)
, (9,−4)
(
9
,
−
4
)
, and (7,−6)
(
7
,
−
6
)
. Using the coordinates, what is the approximate area of the rectangle? (1 point)
Responses

26.08 units2
26.08

units
2
26.07 units squared

24.1 units2
24.1

units
2
24.1 units squared

52.2 units2
52.2

units
2
52.2 units squared

12.05 units2

Answer 1

Use the shoelace formula (or the cross product of adjacent side vectors).

Order the vertices (0,0), (2,2), (9,−4), (7,−6):
sum1 = 0·2 + 2·(−4) + 9·(−6) + 7·0 = −62
sum2 = 0·2 + 2·9 + (−4)·7 + (−6)·0 = −10
Area = 1/2 |sum1 − sum2| = 1/2 |−62 − (−10)| = 1/2 · 52 = 26

So the area is 26 units^2 (approx. 26.08 rounded), so choose 26.08 units^2.