Question

The number of points on x axis, which are at a distance of 2 units from (2,4) is

Answer 1

Answer:

one point

There is only one point which is at a distance of 2 units from (2,4) on x axis . That is the perpendicular to x-axis !

Step-by-step explanation:

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Answer 2

SOLUTION

TO DETERMINE

The number of points on x axis, which are at a distance of 2 units from (2,4)

CONCEPT TO BE IMPLEMENTED

For the given two points $\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$ the distance between the points

$= \sf{ \sqrt{ {(x_2 -x_1 )}^{2} + {(y_2 -y_1 )}^{2} } }$

EVALUATION

Let us consider the point on x axis as (h, 0)

Then by the given condition

Distance between (h, 0) and (2,4) = 2 unit

$\displaystyle \sf{ \implies \sqrt{ {(h - 2)}^{2} + {(0 - 4)}^{2} } = 2 }$

$\displaystyle \sf{ \implies \sqrt{ {(h - 2)}^{2} + {(4)}^{2} } = 2 }$

$\displaystyle \sf{ \implies {(h - 2)}^{2} + 16 = 4 }$

$\displaystyle \sf{ \implies {(h - 2)}^{2} = - 12 }$

Since square of any real number can not be negative

So we can not get any real value of h from above equation

Hence there does not exist any point on x axis, which are at a distance of 2 units from (2,4)

FINAL ANSWER

The number of points on x axis, which are at a distance of 2 units from (2,4) is 0 ( Zero )

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