What is the distance from the point (3, 4) to the line x + y = 5? (2022)

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Question: What is the distance from the point (3, 4) to the line x + y = 5? (2022)

Options:

Correct Answer: 2

Solution:

Distance = |3 + 4 - 5| / √(1² + 1²) = |2| / √2 = 2/√2 = √2.

What is the distance from the point (3, 4) to the line x + y = 5? (2022)

What is the distance from the point (3, 4) to the line x + y = 5? (2022)

Step 1: Identify the point from which we want to find the distance. The point is (3, 4).
Step 2: Write down the equation of the line. The line is given as x + y = 5.
Step 3: Rearrange the line equation into the form Ax + By + C = 0. This gives us: 1x + 1y - 5 = 0, where A = 1, B = 1, and C = -5.
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, y0) = (3, 4), A = 1, B = 1, and C = -5.
Step 6: Calculate the numerator: |1*3 + 1*4 - 5| = |3 + 4 - 5| = |2| = 2.
Step 7: Calculate the denominator: √(1² + 1²) = √(1 + 1) = √2.
Step 8: Divide the numerator by the denominator: Distance = 2 / √2.
Step 9: Simplify the distance: 2 / √2 = √2.

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