Question

find x if distance between points L(x,7) and M(1,15)is 10​

Answer 1

D² = ( y2 – y1 )² + ( x2 – x1 )²

( 10 )² = ( 15 – 7 )² + ( 1 – x )²

100 = 8² + ( 1 – x )²

100 – 64 = ( 1 – x )²

36 = ( 1 – x )²

6² = ( 1– x )²

sq root both sides

6 = 1 – x

x = 1 – 6

x = – 5

Answer 2

Answer:

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

$\\ \longrightarrow \sf{10 = \sqrt {{( 1 - x)}^{2} + {(15 - 7)}^{2}}}$

$\\ \longrightarrow \sf{10 = \sqrt {{( 1 - x)}^{2} + {(8)}^{2}}}$

$\\ \longrightarrow \sf{10 = \sqrt {{( 1 - x)}^{2} + 64}}$

$\\ \longrightarrow \sf{100 = {( 1 - x)}^{2} + 64}$

$\\ \longrightarrow \sf{100 - 64 = {( 1 - x)}^{2}}$

$\\ \longrightarrow \sf{36 = {( 1 - x)}^{2}}$

Taking square root on both sides

$\\ \longrightarrow \sf{\sqrt {36} = \sqrt {{( 1 - x)}^{2}}}$

$\\ \longrightarrow \sf{ +\:or\:- 6 = 1 - x }$

$\\ \longrightarrow \sf{ 1 - x = 6\: or 1 - x = -6 }$

$\\ \longrightarrow \sf{ - x = 6 - 1 \: or \:- x = -6 - 1}$

$\\ \longrightarrow \sf{ - x = 5 \: or \:- x = -7}$

$\\ \longrightarrow \sf{ x = -5 \: or \: x = 7}$

hope it helps you