What is the distance from the point (2, 3) to the line x + y = 5? (2020)

What is the distance from the point (2, 3) to the line x + y = 5? (2020)

Step 1: Identify the point from which we want to find the distance. The point is (2, 3).
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 standard form Ax + By + C = 0. This gives us 1*x + 1*y - 5 = 0.
Step 4: Identify the coefficients A, B, and C from the standard form. Here, A = 1, B = 1, and C = -5.
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 point (2, 3) into the formula. Here, x0 = 2 and y0 = 3.
Step 7: Calculate the numerator: |(1*2 + 1*3 - 5)| = |(2 + 3 - 5)| = |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 distance: 0 / √2 = 0.

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