Question

a quadrillateral has sides with equations y = -2x, 2x+y=6, y=1/2x+6, and x-2y=9. is the figure a rectangle? explain your reasoning

Answer 1

A) y = -2x  ⇒ slope (m) = $\frac{-2}{1}$

B)  2x + y = 6

   -2x        -2x  

            y = -2x + 6  ⇒ slope (m) = $\frac{-2}{1}$

C) y = $\frac{1}{2}$x + 6  ⇒  slope (m) = $\frac{1}{2}$

D) x - 2y = 9

  -x           -x  

      -2y = -x + 9

      $\frac{-2}{-2}$y = $\frac{-1}{-2}$x + $\frac{9}{-2}$

         y =  $\frac{1}{2}$x - 4.5  ⇒  slope (m) = $\frac{1}{2}$

A rectangle has 90° angles so two slopes must be the same and the other two slopes must be perpendicular (opposite sign and reciprocal) to the first two slopes.

Slopes:  $\frac{-2}{1}$, $\frac{-2}{1}$, $\frac{1}{2}$, $\frac{1}{2}$.

Answer: YES.  Two lines have a slope of $\frac{1}{2}$and the other two lines have a perpendicular slope of $\frac{-2}{1}$,