JEE Exam > JEE Questions > Let A(2, 12) and B(6,4) be two points. The sl... Start Learning for Free
Let A(2, 12) and B(6,4) be two points. The slope of a line perpendicular to the line AB is:
- a)2
- b)-2
- c)1/2
- d)-1/2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let A(2, 12) and B(6,4) be two points. The slope of a line perpendicul...
Slope of the points A and B is -2 and the lines are perpendicular then
m1×m2 = -1.
∴ the slope is 1/2
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Let A(2, 12) and B(6,4) be two points. The slope of a line perpendicul...
Explanation:
The slope of a line perpendicular to a given line with slope m is -1/m. So, to find the slope of a line perpendicular to AB, we need to first find the slope of AB.
Step 1: Find the slope of AB
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Using this formula, we can find the slope of AB as:
mAB = (4 - 12) / (6 - 2) = -8 / 4 = -2
Step 2: Find the slope of a line perpendicular to AB
The slope of a line perpendicular to AB is given by:
mperp = -1/mAB
Substituting the value of mAB, we get:
mperp = -1/-2 = 1/2
Therefore, the slope of a line perpendicular to AB is 1/2.
Answer: Option C. 1/2.
The slope of a line perpendicular to a given line with slope m is -1/m. So, to find the slope of a line perpendicular to AB, we need to first find the slope of AB.
Step 1: Find the slope of AB
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
Using this formula, we can find the slope of AB as:
mAB = (4 - 12) / (6 - 2) = -8 / 4 = -2
Step 2: Find the slope of a line perpendicular to AB
The slope of a line perpendicular to AB is given by:
mperp = -1/mAB
Substituting the value of mAB, we get:
mperp = -1/-2 = 1/2
Therefore, the slope of a line perpendicular to AB is 1/2.
Answer: Option C. 1/2.
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