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The point on x-axis which is equidistant from (5,9) and (-4,6) is
- a)(3,0)
- b)(1,0)
- c)(2,0)
- d)(4,1)
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The point on x-axis which is equidistant from (5,9) and (-4,6) is̴...
for 2 points to be equidistant to 2 another the length of the line drawn to them should the first two should be equal to the next two.
let that point be (x,0) (y=0 as it leis on the x axis)
using distance formula-
root of ((x+4)2 +(0-6)2)=root of ((x-5)2 +(0-9)2)
squaring both sides and opening the brackets we get-
x2 + 8x + 16 + 36 = x2 - 10x + 25 +81
bring variables to one side and constants to another we get-
18x = 54
x = 54/18 = 3
therefore x = 3 and y =0 (since it leis in the x axis)
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The point on x-axis which is equidistant from (5,9) and (-4,6) is̴...
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The point on x-axis which is equidistant from (5,9) and (-4,6) is̴...
To find the point on the x-axis that is equidistant from two given points, we need to find the midpoint of the line segment connecting the two points.
- Let's find the midpoint using the formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Given points: (5,9) and (-4,6)
Using the formula, we can calculate the midpoint as:
Midpoint = ((5 + (-4))/2, (9 + 6)/2)
= (1/2, 15/2)
= (0.5, 7.5)
- Since we want to find a point on the x-axis, the y-coordinate of the midpoint should be zero.
- Therefore, the x-coordinate of the midpoint is the point that is equidistant from the given points on the x-axis.
Now, let's check which option satisfies this condition.
- Option A: (3,0)
The x-coordinate of the midpoint is 0.5, which is not equal to 3. Therefore, this option is not correct.
- Option B: (1,0)
The x-coordinate of the midpoint is 0.5, which is not equal to 1. Therefore, this option is not correct.
- Option C: (2,0)
The x-coordinate of the midpoint is 0.5, which is not equal to 2. Therefore, this option is not correct.
- Option D: (4,1)
The x-coordinate of the midpoint is 0.5, which is not equal to 4. Therefore, this option is not correct.
- None of the given options satisfy the condition.
- It seems that none of the given options are correct. There might be an error in the question or options provided. Please double-check the question and options.
- Let's find the midpoint using the formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Given points: (5,9) and (-4,6)
Using the formula, we can calculate the midpoint as:
Midpoint = ((5 + (-4))/2, (9 + 6)/2)
= (1/2, 15/2)
= (0.5, 7.5)
- Since we want to find a point on the x-axis, the y-coordinate of the midpoint should be zero.
- Therefore, the x-coordinate of the midpoint is the point that is equidistant from the given points on the x-axis.
Now, let's check which option satisfies this condition.
- Option A: (3,0)
The x-coordinate of the midpoint is 0.5, which is not equal to 3. Therefore, this option is not correct.
- Option B: (1,0)
The x-coordinate of the midpoint is 0.5, which is not equal to 1. Therefore, this option is not correct.
- Option C: (2,0)
The x-coordinate of the midpoint is 0.5, which is not equal to 2. Therefore, this option is not correct.
- Option D: (4,1)
The x-coordinate of the midpoint is 0.5, which is not equal to 4. Therefore, this option is not correct.
- None of the given options satisfy the condition.
- It seems that none of the given options are correct. There might be an error in the question or options provided. Please double-check the question and options.
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