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In a rectangular coordinate system, what is the area of a rhombus whos 30 Jun 2016, 07:56
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76% (01:49) correct 24% (01:38) wrong based on 111 sessions

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In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (8, 0), (0, -3.5), (-8, 0)?

A. 56
B. 88
C. 112
D. 116
E. 120
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A
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In a rectangular coordinate system, what is the area of a rhombus whos 30 Jun 2016, 08:13
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Answer is A : 56

Refer to diagram, and it can be broken down to 4 identical triangles with base as 8 and height as 3.5.
So total area =\(4 * 1/2 * 8 * 3.5 = 56\)
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In a rectangular coordinate system, what is the area of a rhombus whos 30 Jun 2016, 09:14
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In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (8, 0), (0, -3.5), (-8, 0)?

A. 56
B. 88
C. 112
D. 116
E. 120
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Ares of rhombus= 1/2* D1 *D2

Length of 1st diagonal = 8+8= 16
Length of 2nd diagonal= 3.5+3.5= 7

Area= 1/2*16*7= 56

A is the answer
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In a rectangular coordinate system, what is the area of a rhombus whos 30 Jun 2016, 10:02
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area is also given by (1/2)*d1*d2 (where d1 and d2 are the two diagonals)
here,
d1 = distance between points on x axis = |-8| + |8| =16
d2 = distance between points on y axis = |-3.5| + |3.5| =7

area = 112/2 = 56
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In a rectangular coordinate system, what is the area of a rhombus whos 14 Mar 2019, 17:12
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Bunuel
In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (8, 0), (0, -3.5), (-8, 0)?

A. 56
B. 88
C. 112
D. 116
E. 120
Show more

We see that two of the vertices are on the x-axis, and the other two are on the y-axis. Thus, the rhombus is a diamond-shaped rhombus on the xy-plane. Furthermore, the segment connecting the two vertices on the x-axis is one diagonal of the rhombus, and the segment connecting the two vertices on the y-axis is the other diagonal.

We see the the diagonal on the x-axis has length of 8 - (-8) = 16 and the one on the y-axis has length of 3.5 - (-3.5) = 7. Since the area of a rhombus is half of the product of its diagonals, the area of this rhombus is:

1/2 x 16 x 7 = 56

Answer: A
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