Question

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

Answer 1

lets use distance formulae to find out x

[√(x-1)²+(7-15)²]=10

[√(x²+1-2x)+64]=10

x²+1-2x+64=100(squaring both sides)

x²-2x-35=0

x²-7x+5x-35=0

x(x-7)+5(x-7)=0

(x-7)(x+5)=0

so x=7 or -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