Class 9 Exam > Class 9 Questions > If two points M and N lie on y-axis, and have...
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If two points M and N lie on y-axis, and have same absolute value of abscissa but different signs. If the abscissa of point M is K, then the distance between M and N is equal to :
- a)|K|
- b)|2K| = 2|K|
- c)2K
- d)4 |K|
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If two points M and N lie on y-axis, and have same absolute value of a...
Let the coordinates of point M be (0, k)
{∵ M is on y-axis}
∴ Coordinates of point N = (0 ,- K)
∴ Distance between point M and N
= | K - (-K)| = 2|K|
{∵ M is on y-axis}
∴ Coordinates of point N = (0 ,- K)
∴ Distance between point M and N
= | K - (-K)| = 2|K|
Community Answer
If two points M and N lie on y-axis, and have same absolute value of a...
Explanation:
Given Information:
- Points M and N lie on the y-axis.
- Both points have the same absolute value of abscissa but different signs.
- The abscissa of point M is K.
Distance between Points M and N:
- The distance between two points on a plane is given by the formula: Distance = √((x2 - x1)^2 + (y2 - y1)^2)
- Since points M and N lie on the y-axis, their y-coordinates are the same.
- The x-coordinate of point M is K, and the x-coordinate of point N is -K (as they have the same absolute value but different signs).
- Substituting the coordinates of points M and N into the distance formula:
Distance = √(((-K) - K)^2 + (y - y)^2)
Distance = √((-2K)^2)
Distance = √(4K^2)
Distance = 2|K|
Therefore, the distance between points M and N is equal to |2K|, which is the correct answer.
Given Information:
- Points M and N lie on the y-axis.
- Both points have the same absolute value of abscissa but different signs.
- The abscissa of point M is K.
Distance between Points M and N:
- The distance between two points on a plane is given by the formula: Distance = √((x2 - x1)^2 + (y2 - y1)^2)
- Since points M and N lie on the y-axis, their y-coordinates are the same.
- The x-coordinate of point M is K, and the x-coordinate of point N is -K (as they have the same absolute value but different signs).
- Substituting the coordinates of points M and N into the distance formula:
Distance = √(((-K) - K)^2 + (y - y)^2)
Distance = √((-2K)^2)
Distance = √(4K^2)
Distance = 2|K|
Therefore, the distance between points M and N is equal to |2K|, which is the correct answer.
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If two points M and N lie on y-axis, and have same absolute value of abscissa but different signs. If the abscissa of point M is K, then the distance between M and N is equal to :a)|K|b)|2K| = 2|K|c)2Kd)4 |K|Correct answer is option 'B'. Can you explain this answer?
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