Question

calculeaza lungimea segmentului ab in fiecare dintre cazuri:A(1,5);B(4,5);A(2,-5),B(2,7);A(3,1)B(-1,4);A(-2,-5)B(3,7);A(5,4);B(-3,-2);A(1,-8);B(-5,0)

Answer 1

1. 3; 2. 12; 3. 5; 4. 13; 5. 10; 6. 10

Explanation:

We can use the distance formula to calculate the lengths of the line segments.

`d = \sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)}`

1. A (1,5), B (4,5) (red)

`d = \sqrt{(x_(2) - x_(1)^(2)) + (y_(2) - y_(1))^(2)} = \sqrt{(4 - 1)^(2) + (5 - 5)^(2)}\\= \sqrt{3^(2) + 0^(2)} = √(9 + 0) = √(9) = \mathbf{3}`

2. A (2,-5), B (2,7) (blue)

`d = \sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)} = \sqrt{(2 - 2)^(2) + (7 - (-5))^(2)}\\= \sqrt{0^(2) + 12^(2)} = √(0 + 144) = √(144) = \mathbf{12}`

3. A (3,1), B (-1,4 ) (green)

`d = \sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)} = \sqrt{(-1 - 3)^(2) + (4 - 1)^(2)}\\= \sqrt{(-4)^(2) + 3^(2)} = √(16 + 9) = √(25) = \mathbf{5}`

4. A (-2,-5), B (3,7) (orange)

`d = \sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)} = \sqrt{(3 - (-2))^(2) + (7 - (-5))^(2)}\\= \sqrt{5^(2) + 12^(2)} = √(25 + 144) = √(169) = \mathbf{13}`

5. A (5,4), B (-3,-2) (purple)

`d = \sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)} = \sqrt{(-3 - 5)^(2) + (-2 - 4)^(2)}\\= \sqrt{(-8)^(2) + (-6)^(2)} = √(64 + 36) = √(100) = \mathbf{10}`

6. A (1,-8), B (-5,0) (black)

`d = \sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2)} = \sqrt{(-5 - 1)^(2) + (0 - (-8))^(2)}\\-= \sqrt{(-6)^(2) + (-8)^(2)} = √(36 + 64) = √(100) = \mathbf{10}`