Answer:
AB and CD are congruent.
Step-by-step explanation:
Given points:
- A = (-4, 1)
- B = (-4, 8)
- C = (-2, -5)
- D = (5, -5)
After plotting the given points (see attachment), we can easily determine that AB is 7 units and CD is 7 units. Therefore, AB and CD are congruent.
Alternatively, as points A and B share the same x-coordinate, the length of AB is the difference between the y-coordinates:
⇒ AB = 8 - 1 = 7 units
Similarly, as points C and D share the same y-coordinate, the length of CD is the difference between the x-coordinates:
⇒ CD = 5 - (-2) = 7 units
Finally, we can prove that AB and CD are congruent by calculating their lengths using the distance formula.
[tex]\boxed{\begin{minipage}{7.8 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]
[tex]\begin{aligned}\implies AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(-4-(-4))^2+(8-1)^2}\\& =\sqrt{(0)^2+(7)^2}\\& =\sqrt{0+49}\\& =\sqrt{49}\\& =7\end{aligned}[/tex]
[tex]\begin{aligned}\implies CD & =\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\ & =\sqrt{(5-(-2))^2+(-5-(-5))^2}\\ & =\sqrt{(7)^2+(0)^2}\\ & =\sqrt{49+0}\\ & =\sqrt{49}\\ & =7\end{aligned}[/tex]
Therefore, as AB = CD, this proves that AB and CD are congruent.
