Answer:
#1) are equal; #2) are NOT opposite reciprocals
Step-by-step explanation:
To find the slopes, we use the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For the slope from A to B,
m = (-3--6)/(2-8) = (-3+6)/(-6) = 3/-6 = -0.5
For the slope from B to C,
m = (-6--3)/(8-14) = (-6+3)/(-6) = -3/-6 = 0.5
For the slope from C to D,
m = (-3-0)/(14-8) = -3/6 = =-0.5
For the slope from D to A,
m = (0--3)/(8-2) = (0+3)/6 = 3/6 = 0.5
The slopes are NOT negative reciprocals.
To find the distances, we use the formula
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
For the distance from A to B,
[tex]d=\sqrt{(-3--6)^2+(2-8)^2}=\sqrt{(-3+6)^2+(-6)^2}=\sqrt{3^2+(-6)^2}\\\\=\sqrt{9+36}=\sqrt{45}=3\sqrt{5}[/tex]
For the distance from B to C,
[tex]d=\sqrt{(-6--3)^2+(8-14)^2}=\sqrt{(-6+3)^2+(-6)^2}=\sqrt{(-3)^2+(-6)^2}\\\\=\sqrt{9+36}=\sqrt{45}=3\sqrt{5}[/tex]
For the distance from C to D,
[tex]d=\sqrt{(-3-0)^2+(14-8)^2}=\sqrt{(-3)^2+6^2}=\sqrt{9+36}=\sqrt{45}\\\\=3\sqrt{5}[/tex]
For the distance from D to A,
[tex]d=\sqrt{(0--3)^2+(8-2)^2}=\sqrt{(0+3)^2+6^2}=\sqrt{3^2+6^2}\\\\=\sqrt{9+36}=\sqrt{45}=3\sqrt{5}[/tex]
The lengths of two consecutive sides are the same.
