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In the rectangular coordinate plane, point A has coordinates
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10 Dec 2020, 12:14
10 Dec 2020, 12:14
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Question Stats:
56% (01:11) correct
44% (01:00) wrong based on 25 sessions
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In the rectangular coordinate plane, point A has coordinates (-4, 0), point B has coordinates (0, 4), point C has coordinates (4, 0), and point D has coordinates (0, -4). What is the area of quadrilateral ABCD?
(A) 8
(B) 16
(C) 24
(D) 32
(E) 64
Kudos for the right answer and explanation
(A) 8
(B) 16
(C) 24
(D) 32
(E) 64
Kudos for the right answer and explanation
Re: In the rectangular coordinate plane, point A has coordinates
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11 Dec 2020, 13:37
11 Dec 2020, 13:37
1
When drawing this our we quickly come to realize that we can utilize the area of a rhombus (or a kite) which is 1/2 * diagonal length 1 * diagonal length 2 which is 1/2 * 8 * 8 = 32.
We get 8 by realizing that points B and D (y axis) are 8 apart and points A and C (x axis) are 8 apart.
Additionally you could use the area of a square and use the distance formula to find one side length and square it to get 32. But this method is a bit more tedious since we'd have to use the distance formula, more time consuming as well.
We get 8 by realizing that points B and D (y axis) are 8 apart and points A and C (x axis) are 8 apart.
Additionally you could use the area of a square and use the distance formula to find one side length and square it to get 32. But this method is a bit more tedious since we'd have to use the distance formula, more time consuming as well.
Re: In the rectangular coordinate plane, point A has coordinates
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18 Sep 2023, 02:06
18 Sep 2023, 02:06
1
Finding the 4 points on the plane, you can imagine the graph as a square with side of 4, or 4 Isosceles right triangles. sticking to the later, the area of each triangle is:
S=0.5*4*4=8
and as there are four of them, the area of the graph is:
4*S=4*8=32
S=0.5*4*4=8
and as there are four of them, the area of the graph is:
4*S=4*8=32
