Carcass wrote:
If \(mx + qy − nx − py = 0\), \(p − q = 2\), and \(\frac{y}{x}=- \frac{1}{3}\) , then which of the following is true?
A. \(n-m=\frac{2}{3}\)
B. \(n-m=- \frac{2}{3}\)
C. \(m+n=\frac{2}{3}\)
D. \(m+n=\frac{3}{2}\)
E. \(m+n= - \frac{3}{2}\)
Tricky!!!
First notice that we can perform some factoring
in partsWe'll start by rearranging the terms to get some like terms together.
Take: \(mx + qy − nx − py = 0\)
Rearrange to get: \(mx − nx + qy − py = 0\)
Factor in parts to get: \(x(m − n) + y(q - p) = 0\)
Now subtract \(y(q - p)\) from both sides to get: \(x(m − n) = -y(q - p)\)
Rewrite the right side of the equation as follows: \(x(m − n) = y(-q + p)\)
Simplify to get: \(x(m − n) = y(p - q)\)
Divide both sides by \(x\) to get: \(m − n = \frac{y(p - q)}{x}\)
Rewrite the right side of the equation to get: \(m − n = \frac{y}{x}(p - q)\)
Replace \(p − q\), and \(\frac{y}{x}\) to get: \(m − n = -\frac{1}{3}(2)\)
Simplify to get: \(m − n = -\frac{2}{3}\)
Multiply both sides by \(-1\) to get: \(-m + n = \frac{2}{3}\)
Finally, rewrite as follows: \(n - m = \frac{2}{3}\)
Answer: A
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep