The distance from the point (1, 2) to the line 2x + 3y - 6 = 0 is:
Practice Questions
Q1
The distance from the point (1, 2) to the line 2x + 3y - 6 = 0 is:
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Questions & Step-by-Step Solutions
The distance from the point (1, 2) to the line 2x + 3y - 6 = 0 is:
Step 1: Identify the point from which you want to find the distance. Here, the point is (1, 2).
Step 2: Write down the equation of the line. The line is given as 2x + 3y - 6 = 0.
Step 3: Substitute the x and y coordinates of the point (1, 2) into the line equation. This means you will calculate 2(1) + 3(2) - 6.
Step 4: Calculate the result of the substitution: 2(1) = 2, 3(2) = 6, so 2 + 6 - 6 = 2.
Step 5: Take the absolute value of the result from Step 4. The absolute value of 2 is |2| = 2.
Step 6: 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. Here, the coefficients are 2 and 3, so calculate √(2² + 3²) = √(4 + 9) = √13.
Step 7: Divide the absolute value from Step 5 by the result from Step 6. This gives you Distance = 2 / √13.
