Question

A line segment of 5 cm if the coordinates of its one end or (2,2) and that of ther end are ( -1,x ) find value of x

Answer 1

Here is your required solution :-

Answer 2

Answer:

$x=6\: Or \: x = -2$

Explanation:

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We know that,

The distance between two points $A(x_{1},y_{1}) \: and B(x_{2},y_{2})\\=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

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Now ,here

Let the coordinates a line segment one end point $A(x_{1},y_{1})=(2,2) \\\: and\: another \: end\: point \\\: B(x_{2},y_{2})=(-1,x)$\\

$Distance (AB) = 5 \: cm$ \* given *\

$\implies AB^{2} = (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$

$\implies (-1-2)^{2}+(x-2)^{2}=5^{2}$

$\implies 3^{2}+(x-2)^{2}=25$

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

$\implies (x-2)^{2}=25-9$

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

$\implies (x-2)=±\sqrt{4^{2}}$

$\implies x-2=±4$

$\implies x-2=4\: Or \: x-2 = -4$

$\implies x=4+2\: Or \: x = -4+2$

$\implies x=6\: Or \: x = -2$

Therefore,

$x=6\: Or \: x = -2$

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