Determine the distance from the point (1, 2) to the line 2x + 3y - 6 = 0. (2023)

₹0.0

Question: Determine the distance from the point (1, 2) to the line 2x + 3y - 6 = 0. (2023)

Options:

Correct Answer: 2

Exam Year: 2023

Solution:

Using the formula for distance from a point to a line, the distance is |2(1) + 3(2) - 6| / sqrt(2^2 + 3^2) = 1.

Determine the distance from the point (1, 2) to the line 2x + 3y - 6 = 0. (2023)

Determine the distance from the point (1, 2) to the line 2x + 3y - 6 = 0. (2023)

Step 1: Identify the point and the line. The point is (1, 2) and the line is given by the equation 2x + 3y - 6 = 0.
Step 2: Write down the formula for the distance from a point (x0, y0) to a line Ax + By + C = 0. The formula is: Distance = |Ax0 + By0 + C| / sqrt(A^2 + B^2).
Step 3: Identify A, B, and C from the line equation. Here, A = 2, B = 3, and C = -6.
Step 4: Substitute the coordinates of the point (1, 2) into the formula. So, x0 = 1 and y0 = 2.
Step 5: Calculate the numerator: |2(1) + 3(2) - 6|. This simplifies to |2 + 6 - 6| = |2| = 2.
Step 6: Calculate the denominator: sqrt(2^2 + 3^2). This simplifies to sqrt(4 + 9) = sqrt(13).
Step 7: Now, put the numerator and denominator together: Distance = 2 / sqrt(13).
Step 8: To find the approximate distance, you can calculate 2 / sqrt(13) which is approximately 0.5547.

Distance from a Point to a Line – This concept involves using the formula to calculate the perpendicular distance from a given point to a specified line in a two-dimensional space.