What is the distance from the point (1, 1) to the line x + y = 2? (2023)

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Question: What is the distance from the point (1, 1) to the line x + y = 2? (2023)

Options:

Correct Answer: 1

Exam Year: 2023

Solution:

Distance = |1 + 1 - 2| / √(1² + 1²) = 0 / √2 = 0.

What is the distance from the point (1, 1) to the line x + y = 2? (2023)

What is the distance from the point (1, 1) to the line x + y = 2? (2023)

Step 1: Identify the point we are measuring from, which is (1, 1).
Step 2: Write down the equation of the line, which is x + y = 2.
Step 3: Rearrange the line equation to the form Ax + By + C = 0. This gives us: 1x + 1y - 2 = 0.
Step 4: Identify A, B, and C from the line equation. Here, A = 1, B = 1, and C = -2.
Step 5: Use the distance formula from a point (x0, y0) to a line Ax + By + C = 0, which is: Distance = |Ax0 + By0 + C| / √(A² + B²).
Step 6: Substitute the values into the formula. Here, (x0, y0) = (1, 1), so we calculate: |1*1 + 1*1 - 2|.
Step 7: Simplify the expression: |1 + 1 - 2| = |0| = 0.
Step 8: Calculate the denominator: √(1² + 1²) = √(1 + 1) = √2.
Step 9: Now, plug the values into the distance formula: Distance = 0 / √2.
Step 10: Simplify the final result: Distance = 0.

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