Math, asked by logicgate2115, 10 months ago

If the distance between the points A(2, -2) and B(-1, ) is 5, then

Answers

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

$\huge\boxed{x = - 6}$ or $\huge\boxed{x = 2}$

$\LARGE{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\LARGE{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$

Two points

A ( 2 , -2) , and
B ( -1 , x )

and, AB = 5 units

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$

x is to be found.

$\LARGE{\underline{\mathtt{\textcolor{teal}{Construction :-}}}}$

Have a look on the attachment.

$\LARGE{\underline{\mathtt{\textcolor{teal}{Concept \: \: used :-}}}}$

Coordinate Geometry and Distance formula

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

let,

$A(2,-2) = A(x_1,y_1)$ , and
$B(-1, x ) = A(x_2,y_2)$

Now, A/Q,

$AB = 5 \: units$

$\Rightarrow \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } = 5$

On squaring both the sides, we get :

$\Rightarrow {[ \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } ]}^{2} = {[5]}^{2}$

$\Rightarrow {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} = 25$

$\Rightarrow {( - 1 - 2)}^{2} + {(x - ( - 2))}^{2} = 25$

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

$\Rightarrow 9 + {x}^{2} + 4 + 4x = 25$

$\Rightarrow {x}^{2} + 4x + 13 = 25$

$\Rightarrow {x}^{2} + 4x + 13 - 25 = 0$

$\Rightarrow {x}^{2} + 4x - 12 = 0$

$\Rightarrow {x}^{2} + (6 - 4)x - 12 = 0$

$\Rightarrow {x}^{2} + 6x - 2x - 12 = 0$

$\Rightarrow x(x + 6) - 2(x + 6) = 0$

$\Rightarrow (x + 6)(x - 12) = 0$

$\Rightarrow (x + 6) = 0$ | or, $(x - 2) = 0$

$\Rightarrow x = - 6 \: \: \: \: \: \: \: \:$ | $\Rightarrow x = 2$

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

The B coordinate is either ( -1. -6) or ( -1, 2).

$\rule{3mm}{.1pt}%$

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