Answer:
- Equal midpoints of AC and BC.
- The product of the slopes of the diagonals AC and DB is -1.
Step-by-step explanation:
1. Plot the given points, as you can see in the graph attached.
2. Calculate the midpoint of AC and DB:
[tex]M_{AC}=(\frac{-5+(-1)}{2},\frac{-1+5}{2})=(-3,2)\\M_{DB}=(\frac{-9+3}{2},\frac{6+(-2)}{2})=(-3,2)[/tex]
Therefore, the midpoint of AC and DB are equal.
3. Calculte the slope of the diagonals AC and DB:
[tex]m_{AC}=\frac{5-(-1)}{-1-(-5)}=\frac{3}{2}\\m_{DB}=\frac{-2-6)}{3-(-9)}=-\frac{2}{3}[/tex]
4. Multiply the slopes of the diagonals:
[tex](\frac{3}{2})(-\frac{2}{3})=-1[/tex] (AC and DB are perpendicular)
