Question

Find those points on x-axis, each of which is at a distance of 5 units
from the point A(5,-3).

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Answer 1

Given ,

The distance between x axis and (5 , -3) is 5 units

We know that , the distance between two points is given by

$\boxed{ \tt{Distance = \sqrt{ {( x_{2} -x_{1} )}^{2} + {(y_{2} -y_{1})}^{2} } }}$

Thus ,

$5 = \sqrt{ {(5 - x)}^{2} + {( - 3 - 0)}^{2} }$

Squaring on both sides , we get

$\tt 25 = {(5 - x)}^{2} + 9$

$\tt {(5 - x)}^{2} = 16$

Taking square root on both sides , we get

5 - x = ± 4

Thus ,

5 - x = 4 or 5 - x = -4

x = 1 or x = 9

Therefore , the point on the x axis is (1 , 0) or (9 , 0)

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