Question

The distance between the points ( 5, -9 ) and ( 11, y ) is 10 units . Find the values of y. ​

Answer 1

Given : The distance between the points ( 5, -9 ) and ( 11, y ) is 10 units .

Need To Find : The Value of y ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

⠀✇ Formula to Calculate  Distance between two points ( x₁ , y₁ ) and ( x₂ , y₂ ) is Given by — 

$\qquad \star\:\pmb{\underline {\boxed {\sf \: Distance \:=\: \sqrt{ \bigg( x_2 - x_1 \bigg)^2 \: +\:\bigg( y_2 - y_1\:\bigg)^2}\:\:}}}\:$

⠀Where ,

• x₁ = 5 ,

• x₂ =  11 ,

• y₁ = – 9 &

• y₂ = y . 

$\\\qquad \dag\underline {\frak{ Substituting \:known \:Values \:in Formula \:\::\:}}$

$:\implies \sf \: Distance \:=\: \sqrt{ \bigg( x_2 - x_1 \bigg)^2 \: +\:\bigg( y_2 - y_1\:\bigg)^2}\:\: \\\\\\ :\implies \sf \: 10 \:=\: \sqrt{ \bigg( 11 - 5 \bigg)^2 \: +\:\bigg( y - \:\big\{ - 9\big\}\:\bigg)^2}\:\: \\\\\\ :\implies \sf \: 10 \:=\: \sqrt{ 6^2 \: +\:\bigg( y + \: 9 \:\bigg)^2}\:\: \\\\\\ :\implies \sf \: 10 \:=\: \sqrt{ 36 \: +\:\bigg( y + \: 9 \:\bigg)^2}\:\: \\\\\\ :\implies \sf \: 10^2 \:=\: 36 \: +\:\big( y + \: 9 \:\big)^2\:\: \\\\\\ :\implies \sf \: 100 \:-\:36\:=\: \:\big( y + \: 9 \:\big)^2\:\: \\\\\\ :\implies \sf \: 64\:=\: \:\big( y + \: 9 \:\big)^2\:\: \\\\\\ :\implies \sf \: \:\big( y + \: 9 \:\big)^2\:\:=\: 64\: \\\\\\ :\implies \sf \: \:\big( y + \: 9 \:\big)\:\:=\: \pm\sqrt{64}\: \\\\\\ :\implies \sf \: \: y + \: 9 \:\:\:=\: \pm 8\: \\\\\\:\implies \pmb {\underline {\boxed {\purple {\:\frak{ \:y\:\:=\:-1\:or\:-17\:}}}}}\:\bigstar \:$

$\qquad \therefore \:\underline {\sf Hence \:,\:The\:Value \:of\:y\:is\:\pmb{\sf -1\:or\:-17\:}\:.\:}$