The coordinates of the foot of the perpendicular from the point (1, 2) to the li
Practice Questions
Q1
The coordinates of the foot of the perpendicular from the point (1, 2) to the line 3x + 4y = 12 are:
(2, 1)
(1, 2)
(0, 3)
(3, 0)
Questions & Step-by-Step Solutions
The coordinates of the foot of the perpendicular from the point (1, 2) to the line 3x + 4y = 12 are:
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).
