Question

Find x if distance between points L(x,7) and M (1,15) is 17.​

Answer 1

Solution:

$\\ \underline{\dag\;\frak{As\;we\;know\;that:}}\\ \\ \\ \sf{Distance\;between\;two\;points\;=\;\sqrt{\bigg(x_2-x_1\bigg)^2+\bigg(y_2-y_1\bigg)^2}}$

Putting the values on known formula,

$\\ \longrightarrow\;\sf{17\;=\;\sqrt{\bigg(1-x\bigg)^2+\bigg(15-7\bigg)^2}}\\ \\ \\ \longrightarrow\;\sf{17\;=\;\sqrt{\bigg(1-x\bigg)^2+\bigg(8\bigg)^2}}\\ \\ \\ \longrightarrow\;\sf{\;17\;=\;\sqrt{\bigg(1-x\bigg)^2+64}}\\ \\ \\ \longrightarrow\;\sf{17^2\;=\;\bigg(1-x\bigg)^2+64}\\ \\ \\ \longrightarrow\;\sf{289\;=\;\bigg(1-x\bigg)^2+64}\\ \\ \\ \longrightarrow\;\sf{289-64\;=\;\bigg(1-x\bigg)^2}\\ \\ \\ \longrightarrow\;\sf{225\;=\;\bigg(1-x\bigg)^2}\\ \\ \\ \longrightarrow\;\sf{\sqrt{225}\;=\;1-x}$

$\longrightarrow\;\sf{\pm\;15\;=\;1-x}\\ \\ \\ \longrightarrow\;\sf{x\;=\;\pm\;15-1}\\ \\ \\ \longrightarrow\;\sf{x\;=\;-14(or)16}$

Hence,

• The value of x is -14(or)16.

Answer 2

Answer:

LM = $\\ \sf{\sqrt {{( x2 - x1 )}^{2} + {(y2 - y1)}^{2}}}$

$\\ \longrightarrow \sf{17 = \sqrt {{( 1 - x)}^{2} + {(15 - 7)}^{2}}}$

$\\ \longrightarrow \sf{17 = \sqrt {{( 1 - x)}^{2} + {(8)}^{2}}}$

$\\ \longrightarrow \sf{17 = \sqrt {{( 1 - x)}^{2} + 64}}$

$\\ \longrightarrow \sf{289 = {( 1 - x)}^{2} + 64}$

$\\ \longrightarrow \sf{289 - 64= {( 1 - x)}^{2}}$

$\\ \longrightarrow \sf{225 = {( 1 - x)}^{2}}$

Taking square root on both sides

$\\ \longrightarrow \sf{\sqrt {225} = \sqrt {{( 1 - x)}^{2}}}$

$\\ \longrightarrow \sf{ +\:or\:- 15= 1 - x }$

$\\ \longrightarrow \sf{ 1 - x = 15\: or 1 - x = - 15 }$

$\\ \longrightarrow \sf{ - x = 15 - 1 \: or \:- x = -15 - 1}$

$\\ \longrightarrow \sf{ - x = 14 \: or \:- x = - 16}$

$\\ \longrightarrow \sf{ x = - 14 \: or \: x = 16}$

hope it helps you