Question

The midpoint of a segment can be found using the formulas for a directed line segment,

x= (a+b)/2 and y= (a−b)/2. When using these formulas to find a midpoint, which is true?
a) a = 1 and b = 2
b) a = 2 and b = 1
c) a = 1 and a + b = 2
d) a = 2 and a + b = 2

Answer 1

The correct values for 'a' and 'b' to find the midpoint of a segment using the given formulas are a = 2 and b = 1.

Step-by-step explanation:

The midpoint of a segment can be found using the formulas for a directed line segment, x = (a + b) / 2 and y = (a - b) / 2. To determine which values of 'a' and 'b' are correct, we need to use the given options and substitute them into the formulas.

1. a = 1 and b = 2: Substitute these values into the formulas. We get x = (1 + 2) / 2 = 1.5 and y = (1 - 2) / 2 = -0.5. This is not the correct answer.
2. a = 2 and b = 1: Substitute these values into the formulas. We get x = (2 + 1) / 2 = 1.5 and y = (2 - 1) / 2 = 0.5. This is the correct answer.
3. a = 1 and a + b = 2: Substitute 'a = 1' and 'a + b = 2' into the formulas. We get x = (1 + 2) / 2 = 1.5 and y = (1 - 2) / 2 = -0.5. This is not the correct answer.
4. a = 2 and a + b = 2: Substitute 'a = 2' and 'a + b = 2' into the formulas. We get x = (2 + 2) / 2 = 2 and y = (2 - 2) / 2 = 0. This is not the correct answer.

Therefore, the correct values for 'a' and 'b' are a = 2 and b = 1.