What is the distance from the point (2, 3) to the line x + y - 5 = 0? (2022)

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Question: What is the distance from the point (2, 3) to the line x + y - 5 = 0? (2022)

Options:

Correct Answer: 1

Exam Year: 2022

Solution:

Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0

What is the distance from the point (2, 3) to the line x + y - 5 = 0? (2022)

What is the distance from the point (2, 3) to the line x + y - 5 = 0? (2022)

Step 1: Identify the point and the line. The point is (2, 3) and the line is given by the equation x + y - 5 = 0.
Step 2: Rewrite the line equation in the form Ax + By + C = 0. Here, A = 1, B = 1, and C = -5.
Step 3: 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 4: Substitute the values into the formula. Here, x0 = 2, y0 = 3, A = 1, B = 1, and C = -5.
Step 5: Calculate the numerator: |(1*2 + 1*3 - 5)| = |(2 + 3 - 5)| = |0| = 0.
Step 6: Calculate the denominator: √(1² + 1²) = √(1 + 1) = √2.
Step 7: Now, plug the values into the distance formula: Distance = 0 / √2 = 0.
Step 8: Conclude that the distance from the point (2, 3) to the line x + y - 5 = 0 is 0.

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