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The co – ordinates of the mid – point of the line joining the points (3p, 4) and ( – 2, 4) are (5, p). The value of ‘p’ is
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'D'. Can you explain this answer?
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The co – ordinates of the mid – point of the line joining ...
Explanation:
Let the coordinates of midpoint O(5,p) is equidistance from the points A(3p,4) and B(−2,4).( because O is the mid-point of AB)
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The co – ordinates of the mid – point of the line joining ...
To find the coordinates of the midpoint of a line segment, we use the midpoint formula. The formula for finding the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, we are given the coordinates of two points: (3p, 4) and (2, 4). Let's use the midpoint formula to find the coordinates of the midpoint.
- Finding the x-coordinate of the midpoint:
The x-coordinate of the midpoint is given by ((x₁ + x₂) / 2). Plugging in the coordinates, we have:
((3p + 2) / 2) = 5
Simplifying the equation, we get:
3p + 2 = 10
3p = 8
p = 8/3
- Finding the y-coordinate of the midpoint:
The y-coordinate of the midpoint is given by ((y₁ + y₂) / 2). Plugging in the coordinates, we have:
(4 + 4) / 2 = 8 / 2 = 4
So, the y-coordinate of the midpoint is 4.
Therefore, the coordinates of the midpoint are (5, 4p/3).
Since we are given that the y-coordinate of the midpoint is p, we can equate it to 4p/3:
4p/3 = p
Multiplying both sides of the equation by 3, we get:
4p = 3p
p = 0
However, this contradicts with the given information that p is a non-zero value. Therefore, the only possible value for p is 0. Hence, the correct answer is option 'D' (p = 0).
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, we are given the coordinates of two points: (3p, 4) and (2, 4). Let's use the midpoint formula to find the coordinates of the midpoint.
- Finding the x-coordinate of the midpoint:
The x-coordinate of the midpoint is given by ((x₁ + x₂) / 2). Plugging in the coordinates, we have:
((3p + 2) / 2) = 5
Simplifying the equation, we get:
3p + 2 = 10
3p = 8
p = 8/3
- Finding the y-coordinate of the midpoint:
The y-coordinate of the midpoint is given by ((y₁ + y₂) / 2). Plugging in the coordinates, we have:
(4 + 4) / 2 = 8 / 2 = 4
So, the y-coordinate of the midpoint is 4.
Therefore, the coordinates of the midpoint are (5, 4p/3).
Since we are given that the y-coordinate of the midpoint is p, we can equate it to 4p/3:
4p/3 = p
Multiplying both sides of the equation by 3, we get:
4p = 3p
p = 0
However, this contradicts with the given information that p is a non-zero value. Therefore, the only possible value for p is 0. Hence, the correct answer is option 'D' (p = 0).
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The co – ordinates of the mid – point of the line joining the points (3p, 4) and ( – 2, 4) are (5, p). The value of ‘p’ isa)1b)2c)3d)4Correct answer is option 'D'. Can you explain this answer?
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