What is the distance from the point (1, 2) to the line x + y - 3 = 0? (2023)

What is the distance from the point (1, 2) to the line x + y - 3 = 0? (2023)

Step 1: Identify the point from which we want to find the distance. The point is (1, 2).
Step 2: Write down the equation of the line. The line is given as x + y - 3 = 0.
Step 3: Rearrange the line equation to the form Ax + By + C = 0. Here, A = 1, B = 1, and C = -3.
Step 4: 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 5: Substitute the values into the formula. Here, x0 = 1, y0 = 2, A = 1, B = 1, and C = -3.
Step 6: Calculate the numerator: |1*1 + 1*2 - 3| = |1 + 2 - 3| = |0| = 0.
Step 7: Calculate the denominator: √(1² + 1²) = √(1 + 1) = √2.
Step 8: Now, plug the values into the distance formula: Distance = 0 / √2 = 0.
Step 9: Since the distance is 0, it means the point (1, 2) lies on the line.

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