Answer:
It is correct
Step-by-step explanation:
Answer and Step-by-step explanation: The distance between 2 points is the distance of the straight line that passes through both points. It calculated using the following formula:
d = ![\sqrt{(x_{B} - x_{A} )^{2} + (y_{B} - y_{A} )^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7BB%7D%20-%20x_%7BA%7D%20%29%5E%7B2%7D%20%2B%20%28y_%7BB%7D%20-%20y_%7BA%7D%20%20%29%5E%7B2%7D%20%20%7D)
1) For A (2,1) and B(4, -1)
d = ![\sqrt{(4-2)^{2} + (1+1)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%284-2%29%5E%7B2%7D%20%2B%20%281%2B1%29%5E%7B2%7D%20%7D)
d = ![\sqrt{4+4}](https://tex.z-dn.net/?f=%5Csqrt%7B4%2B4%7D)
d = 2![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
2) 5 = ![\sqrt{(0-x)^{2} + (1-2)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%280-x%29%5E%7B2%7D%20%2B%20%281-2%29%5E%7B2%7D%20%7D)
25 = x² + 1
x² = 24
x = 2![\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B6%7D)
3) d = ![\sqrt{(-5-2)^{2} + (-2-5)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28-5-2%29%5E%7B2%7D%20%2B%20%28-2-5%29%5E%7B2%7D%20%7D)
d = ![\sqrt{(-7)^{2} + (-7)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28-7%29%5E%7B2%7D%20%2B%20%28-7%29%5E%7B2%7D%20%7D)
d = 7![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
Answer:
x³ - 5x² + 9x - 5
Step-by-step explanation:
If one root is 2 + i, other has to be 2 - i.
So at least 3 roots, minimum degree is 3
(x - 2 - i)(x - 2 + i)(x - 1)
[(x - 2)² - (i)²](x - 1)
(x² - 4x + 4 + 1)(x - 1)
(x² - 4x + 5)(x - 1)
x³ - 4x² + 5x - x² + 4x - 5
x³ - 5x² + 9x - 5
By the markings on the angles,
A ≅ D
B ≅ F
C ≅ E
So ΔABC ~ ΔDFE . . . . . . . . matches the 3rd selection