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What will be the co-ordinates of foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0?
- a)(1/5,2/5)
- b)(2/25,5/25)
- c)(68/25,-49/25)
- d)(-49/25,68/25)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
What will be the co-ordinates of foot of perpendicular line drawn from...
Given: point (-1,3) and line 3x-4y-16=0
To find: co-ordinates of foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0
Concept used: Equation of line, Distance between point and line, Foot of perpendicular
Solution:
Step 1: Convert the given equation of line in slope-intercept form
3x - 4y - 16 = 0
=> 4y = 3x - 16
=> y = (3/4)x - 4
Step 2: Find the slope of the given line
The slope of the given line is (3/4)
Step 3: Find the slope of the line perpendicular to the given line
The slope of the line perpendicular to the given line is -4/3 (negative reciprocal of the slope of the given line)
Step 4: Write the equation of the line perpendicular to the given line passing through the point (-1,3)
Using point-slope form, the equation of the line perpendicular to the given line passing through the point (-1,3) is:
y - 3 = (-4/3)(x + 1)
=> y = (-4/3)x + (5/3)
Step 5: Find the intersection point of the given line and the perpendicular line
Solving the equations of the two lines, we get:
(3/4)x - 4 = (-4/3)x + (5/3)
=> (25/12)x = (17/3)
=> x = (68/25)
Substituting x in the equation of the perpendicular line, we get:
y = (-4/3)(68/25) + (5/3)
=> y = -49/25
Therefore, the co-ordinates of the foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0 is (68/25,-49/25).
Hence, option (C) is the correct answer.
To find: co-ordinates of foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0
Concept used: Equation of line, Distance between point and line, Foot of perpendicular
Solution:
Step 1: Convert the given equation of line in slope-intercept form
3x - 4y - 16 = 0
=> 4y = 3x - 16
=> y = (3/4)x - 4
Step 2: Find the slope of the given line
The slope of the given line is (3/4)
Step 3: Find the slope of the line perpendicular to the given line
The slope of the line perpendicular to the given line is -4/3 (negative reciprocal of the slope of the given line)
Step 4: Write the equation of the line perpendicular to the given line passing through the point (-1,3)
Using point-slope form, the equation of the line perpendicular to the given line passing through the point (-1,3) is:
y - 3 = (-4/3)(x + 1)
=> y = (-4/3)x + (5/3)
Step 5: Find the intersection point of the given line and the perpendicular line
Solving the equations of the two lines, we get:
(3/4)x - 4 = (-4/3)x + (5/3)
=> (25/12)x = (17/3)
=> x = (68/25)
Substituting x in the equation of the perpendicular line, we get:
y = (-4/3)(68/25) + (5/3)
=> y = -49/25
Therefore, the co-ordinates of the foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0 is (68/25,-49/25).
Hence, option (C) is the correct answer.
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What will be the co-ordinates of foot of perpendicular line drawn from...
The line drawn through the foot of perpendicular will be passing through the given point. the line will be perpendicular to the given line so you can get the slope of the required line from the given line. Now you have the slope and point. Find the equation of the line and then find its solution with the given line. this will give the coordinates of foot of perpendicular.
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What will be the co-ordinates of foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0?a)(1/5,2/5)b)(2/25,5/25)c)(68/25,-49/25)d)(-49/25,68/25)Correct answer is option 'C'. Can you explain this answer?
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