If the points (3, 4) and (X, 1) are equidistant from the origin then the value of x is.
- ((a))
±3
- ((b))
±2√6
- ((c))
±√5
- ((d))
±√6
Show Answer
±2√6
Concept -
For two points to be equidistant from the origin, their distances from the origin must be the same.
The distance between any point (x1, x2) and the origin (�1,�1)Unknown node type: span(�1,�1)Unknown node type: span(�1,�1)Unknown node type: span
(0,0)(0,0)(0,0)
(0,0) is given by the distance formula:
Distance=(�1−0)2+(�1−0)2−−−−−−−−−−−−−−−−−−√=�21+�21−−−−−−−√Distance=(�1−0)2+(�1−0)2−−−−−−−−−−−−−−−−−−√=�21+�21−−−−−−−√Distance=(�1−0)2+(�1−0)2=�12+�12
Distance = (√{(x_1-0)^2+(y_1-0)^2} =√{x_1^2 +y_1^2})
Explanation -
Given one point is (3, 4), the distance of this point from the origin is:
Distance = (√{(3)^2+(4)^2} =√{9+16} = √{25} = 5)
Now, we need to find the value of ���
x for the point (�,1)(�,1)(�,1)
(x,1) to also have a distance of 5 units from the origin.
Using the distance formula again:
Distance = (√{(x)^2+(1)^2} = 5)
Now squaring both side -
⇒ x2 + 1 = 25 ⇒ x2 = 24
⇒ x = ± √ 24 = ± 2√ 6
Distance=�2+12−−−−−−−√=Unknown node type: spanDistance=�2+12−−−−−−−√=Unknown node type: spanDistance=�2+12=Unknown node type: span
Hence option(2) is correct.





















































