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The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is √10, then the coordinates of the point are
- a)(1,2) or (3,6)
- b)(1,2) or (3,5)
- c)(2,1) or (3,6)
- d)(2,1) or (6,3)
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The ordinate of a point is twice its abscissa. If its distance from th...
let the coordinate of that point be P(x,2x).
let the given point (4,3) be Q(4,3).
Then PQ=
Most Upvoted Answer
The ordinate of a point is twice its abscissa. If its distance from th...
To find the distance between two points, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's assume the abscissa of the point is x, so the ordinate would be 2x.
The coordinates of the given point are (4, 3), so x1 = 4 and y1 = 3.
The coordinates of the point we're trying to find the distance to are (x, 2x), so x2 = x and y2 = 2x.
Plugging these values into the distance formula:
Distance = √((x - 4)^2 + (2x - 3)^2)
Simplifying the equation:
Distance = √(x^2 - 8x + 16 + 4x^2 - 12x + 9)
Distance = √(5x^2 - 20x + 25)
We want to find the value of x such that the distance is equal to 5. So, we can set up the equation:
√(5x^2 - 20x + 25) = 5
Squaring both sides of the equation:
5x^2 - 20x + 25 = 25
5x^2 - 20x = 0
Dividing both sides of the equation by 5:
x^2 - 4x = 0
Factoring out an x:
x(x - 4) = 0
Setting each factor equal to zero:
x = 0 or x - 4 = 0
So, the possible values for x are 0 and 4.
If x = 0, then the point would be (0, 0).
If x = 4, then the point would be (4, 8).
Therefore, the possible points that satisfy the given conditions are (0, 0) and (4, 8).
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's assume the abscissa of the point is x, so the ordinate would be 2x.
The coordinates of the given point are (4, 3), so x1 = 4 and y1 = 3.
The coordinates of the point we're trying to find the distance to are (x, 2x), so x2 = x and y2 = 2x.
Plugging these values into the distance formula:
Distance = √((x - 4)^2 + (2x - 3)^2)
Simplifying the equation:
Distance = √(x^2 - 8x + 16 + 4x^2 - 12x + 9)
Distance = √(5x^2 - 20x + 25)
We want to find the value of x such that the distance is equal to 5. So, we can set up the equation:
√(5x^2 - 20x + 25) = 5
Squaring both sides of the equation:
5x^2 - 20x + 25 = 25
5x^2 - 20x = 0
Dividing both sides of the equation by 5:
x^2 - 4x = 0
Factoring out an x:
x(x - 4) = 0
Setting each factor equal to zero:
x = 0 or x - 4 = 0
So, the possible values for x are 0 and 4.
If x = 0, then the point would be (0, 0).
If x = 4, then the point would be (4, 8).
Therefore, the possible points that satisfy the given conditions are (0, 0) and (4, 8).
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Community Answer
The ordinate of a point is twice its abscissa. If its distance from th...
Simple...just from given y coordinate is 2 times of x coordinate...it can only be possible if it is option A
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The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is√10, then the coordinates of the point area)(1,2) or (3,6)b)(1,2) or (3,5)c)(2,1) or (3,6)d)(2,1) or (6,3)Correct answer is option 'A'. Can you explain this answer?
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The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is√10, then the coordinates of the point area)(1,2) or (3,6)b)(1,2) or (3,5)c)(2,1) or (3,6)d)(2,1) or (6,3)Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is√10, then the coordinates of the point area)(1,2) or (3,6)b)(1,2) or (3,5)c)(2,1) or (3,6)d)(2,1) or (6,3)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is√10, then the coordinates of the point area)(1,2) or (3,6)b)(1,2) or (3,5)c)(2,1) or (3,6)d)(2,1) or (6,3)Correct answer is option 'A'. Can you explain this answer?.
The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is√10, then the coordinates of the point area)(1,2) or (3,6)b)(1,2) or (3,5)c)(2,1) or (3,6)d)(2,1) or (6,3)Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is√10, then the coordinates of the point area)(1,2) or (3,6)b)(1,2) or (3,5)c)(2,1) or (3,6)d)(2,1) or (6,3)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is√10, then the coordinates of the point area)(1,2) or (3,6)b)(1,2) or (3,5)c)(2,1) or (3,6)d)(2,1) or (6,3)Correct answer is option 'A'. Can you explain this answer?.
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