What is the distance from the point (1, 2) to the line 3x + 4y - 10 = 0?

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Question: What is the distance from the point (1, 2) to the line 3x + 4y - 10 = 0?

Options:

Correct Answer: 2

Solution:

Distance = |3(1) + 4(2) - 10| / √(3² + 4²) = |3 + 8 - 10| / 5 = 1.

What is the distance from the point (1, 2) to the line 3x + 4y - 10 = 0?

What is the distance from the point (1, 2) to the line 3x + 4y - 10 = 0?

Step 1: Identify the point and the line. The point is (1, 2) and the line is given by the equation 3x + 4y - 10 = 0.
Step 2: Substitute the x and y values of the point into the line equation. Replace x with 1 and y with 2 in the equation 3x + 4y - 10.
Step 3: Calculate the value. This means calculating 3(1) + 4(2) - 10.
Step 4: Perform the multiplication: 3(1) = 3 and 4(2) = 8.
Step 5: Add the results from Step 4: 3 + 8 = 11.
Step 6: Subtract 10 from the result: 11 - 10 = 1.
Step 7: Take the absolute value of the result from Step 6: |1| = 1.
Step 8: Calculate the denominator, which is the square root of the sum of the squares of the coefficients of x and y in the line equation: √(3² + 4²).
Step 9: Calculate 3² = 9 and 4² = 16, then add them: 9 + 16 = 25.
Step 10: Take the square root of 25: √25 = 5.
Step 11: Divide the absolute value from Step 7 by the result from Step 10: 1 / 5.
Step 12: The final result is 1 / 5, which simplifies to 1.

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