Question

find x if the distance between the points (x,1) and (2,3) be 4 units

Answer 1

Answer:

x=6

Step-by-step explanation:

(x,1) (2,3) the difference is (4,0) so add that to (x,1) which would be (6,3)

Answer 2

Answer: The value of x is 1.    

Step-by-step explanation:

Given:The distance between the points (x,1) and (2,3) is 4 units.

To find:We have to find the value of x.

Explanation:

Step 1:The distance two points ($x_{1},y_{1}$) and ($x_{2},y_{2}$) can be calculated by using formula,

⇒$\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }$

where $x_{1}=x$,$y_{1}=1$,$x_{2}=2$ and $y_{2}=3$ respectively.                

Step 2:Substituting the values in above formula we get,

⇒$\sqrt{(2-x)^{2}+(3-1)^{2} }= 5$

⇒$\sqrt{(2-x)^{2}+2^{2} }= 5$

⇒$\sqrt{(2-x)^{2}+4 }= 5$

Step 3:On squaring both sides we get,

⇒$(2-x)^{2}+4= 5$

⇒      $(2-x)^{2}= 5-4$

⇒      $(2-x)^{2}=1$

Step 4:Taking square root both sides we get,

⇒       $(2-x)=\sqrt{1}$

⇒         $2-x=1$

⇒            $-x= 1-2$

⇒            $-x= -1$

⇒               x = 1      

∴ The value of x is 1.        

Concept:The distance formula of two points can be given by

                      $D=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }$

where $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are the coordinates of two points respectively.

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