Question

a rhombus is on a coordinate plane and has one of its sides modeled by the equation 3y - 4x = 35. determine which of the following equations could model the opposite side of the rhombus. Select all that apply.

A. y = 4/3 x + 16/3
B. y - 3 = 3/4 (x - 8)
C. 8x - 6y = 38
D. 9y = 12x - 27/14
E. 2x + y = -5
F. 4x - 3y = 12

Answer 1

Answer:

A. y = 4/3 x + 16/3.

C.  8x - 6y = 38

D. 9y = 12x - 27/4

F. 4x - 3y = 12.

Step-by-step explanation:

A rhombus has parallel opposite sides so the lines will have the same slope as:

3y - 4x = 35    

We convert to slope- intercept form:

3y = 4x + 35

y = 4/3 x + 35/3

- so the slope of this line is 4/3.

Now the opposite side will also have a slope of 4/3 but a different y-intercept.

So A. y = 4/3 x + 16/3  is one of the required equations.

8x - 6y = 38

6y = 8x - 38

y = 4/3 x - 38/6.   (C)

-  The same slope, so this could also be one of the required equations.

9y = 12x - 27/4

y = 4/3 x - 27/36 (D)

- so this could also be one of the required equations.

4x - 3y = 12

3y = 4x - 12

y = 4/3 x - 4.

This is one also (F).

B and E have slopes of 3/4 and -2  so could not be models for the opposite side.

Answer 2

The equation that represent the opposite side of the rhombus is option A, C, D and F.

What is the rhombus?

A rhombus contains parallel opposite sides so the lines should contains the same slope

Since

3y - 4x = 35    

Now

We convert to slope- intercept form:

So,

3y = 4x + 35

$y = 4\div 3 x + 35\div 3$

Hence, the slope of this line is $4\div 3$

Now the opposite side will also have a slope of $4\div 3$ however a different y-intercept.

Now

8x - 6y = 38

6y = 8x - 38

$y = 4\div 3 x - 38\div 6.$

This is also the same slope, so this could also be one of the required equations.

Now

$9y = 12x - 27\div 4\\\\y = 4\div 3 x - 27\div 36$

Now

4x - 3y = 12

3y = 4x - 12

$y = 4\div 3 x - 4.$

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