The coordinates of the foot of the perpendicular from the point (1, 2) to the line 3x + 4y = 12 are:

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Q: The coordinates of the foot of the perpendicular from the point (1, 2) to the line 3x + 4y = 12 are:

Solution: Using the formula for foot of perpendicular, we find the coordinates to be (2, 1).

Steps: 9

Step 1: Identify the point from which we want to drop a perpendicular. In this case, the point is (1, 2).
Step 2: Write down the equation of the line, which is 3x + 4y = 12.
Step 3: Rearrange the line equation into slope-intercept form (y = mx + b) to find the slope. The line can be rewritten as y = (-3/4)x + 3.
Step 4: Determine the slope of the line, which is -3/4.
Step 5: Find the slope of the perpendicular line. The slope of a line perpendicular to another is the negative reciprocal. So, the slope will be 4/3.
Step 6: Use the point-slope form of the equation of a line to write the equation of the perpendicular line passing through (1, 2). The equation is y - 2 = (4/3)(x - 1).
Step 7: Simplify the equation of the perpendicular line to find its y-intercept form.
Step 8: Solve the two equations (the original line and the perpendicular line) simultaneously to find the intersection point, which is the foot of the perpendicular.
Step 9: After solving, you will find the coordinates of the foot of the perpendicular to be (2, 1).