A. True. Summing any rational number with an irrational number leads to an irrational result. The proof is a bit lengthy so I'm leaving it out.
B. True. Adding p/q with r/s leads to (ps+qr)/(qs) which is rational. Keep in mind that q and s cannot be zero.
C. False. One counter example is sqrt(3)*sqrt(12) = sqrt(3*12) = sqrt(36) = 6. This shows the product of two irrational numbers, in this case sqrt(3) and sqrt(12), multiplying to get a rational result 6 = 6/1.
D. True. Multiplying p/q and r/s leads to (p*r)/(q*s) which is rational. Keep in mind that q and s cannot be zero.
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The final answer is choice C
<em>Options:</em>
<em>Rotation of 180° about point B
</em>
<em>Rotation of 90° about point b
</em>
<em>Reflection over the x-axis
</em>
<em>Translation down 2 units</em>
<em></em>
Answer:
Rotation of 180° about point B
<em></em>
Step-by-step explanation:
Considering coordinates of point B
Assume the coordinates of the line at point B is (x,y)
i.e. 
First, we need to determine the slope at point B
Taking coordinates about the origin.
The slope of B is:

Where
--- origin

becomes


Taking the options one after the other:
Option A.
When rotated by 180°, the resulting coordinates of B would be

Taking the slope of B'
The slope of B is:

Where
--- origin

becomes



Notice that the slope of B and B' is the same;

<em>Hence:</em>
<em>Rotation of 180° about point B answers the question</em>
<em></em>
<em>There's no need to check for other options</em>
Answer:
4. 3
The answer is the last option, all you do is reduce
Step-by-step explanation:
rise over run = rise/run = 6/2
reduce,
6/2
3/1
3x
Use formula y = k x and find value of k using any of the coordinates