The distance from the point (3, 4) to the line 2x + 3y - 6 = 0 is:

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Question: The distance from the point (3, 4) to the line 2x + 3y - 6 = 0 is:

Options:

Correct Answer: 2

Solution:

Distance = |2(3) + 3(4) - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13.

The distance from the point (3, 4) to the line 2x + 3y - 6 = 0 is:

The distance from the point (3, 4) to the line 2x + 3y - 6 = 0 is:

Step 1: Identify the point and the line. The point is (3, 4) and the line is given by the equation 2x + 3y - 6 = 0.
Step 2: Substitute the x and y values of the point into the line equation. This means we will calculate 2(3) + 3(4) - 6.
Step 3: Calculate the values. First, calculate 2(3) which is 6. Then calculate 3(4) which is 12. Now add these results: 6 + 12 = 18. Finally, subtract 6: 18 - 6 = 12.
Step 4: Take the absolute value of the result from Step 3. The absolute value of 12 is |12| = 12.
Step 5: 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. The coefficients are 2 and 3. So, calculate √(2² + 3²) = √(4 + 9) = √13.
Step 6: Divide the absolute value from Step 4 by the result from Step 5. This gives us Distance = 12 / √13.

Distance from a Point to a Line – This concept involves using the formula for calculating the perpendicular distance from a point to a line given in standard form.
Line Equation – Understanding how to manipulate and interpret the equation of a line in the form Ax + By + C = 0.
Absolute Value and Square Roots – Applying absolute value and square root operations correctly in the context of distance calculations.