Question

if the distance between two point (x,7)and (3,2)is 10 find the value of x​

Answer 1

Question :–

▪︎ If the distance between two points (x , 7) and (3 , 2) is 10 unit , find the value of x = ?

ANSWER :–

GIVEN :–

• Distance between two points (x , 7) and (3 , 2) is 10 unit.

TO FIND :–

• Find the value of x = ?

SOLUTION :–

• If two points are $\: \: { \bold{( x_{1} , y_{1}) \: \: and \: \: ( x_{2} , y_{2}) }} \: \:$ then Distance is –

$\\ { \huge{\star}} \: \: \large { \green{ \boxed{\bold{Distance = \sqrt{ {{( x_{2} - x_{1} ) }^{2} +( y_{2} - y_{1} ) }^{2} } }}}} \: \:$

• Here –

$\\ \: \: \: \: . \: \: { \blue{ \bold{ x_{1} = x }}} \: \:$

$\\ \: \: \: \: . \: \: { \blue{ \bold{ x_{2} = 3 }}} \: \:$

$\\ \: \: \: \: . \: \: { \blue{ \bold{ y_{1} = 7 }}} \: \:$

$\\ \: \: \: \: . \: \: { \blue{ \bold{ y_{2} = 2 }}} \: \:$

• Now put the values –

$\\ \implies {\bold{Distance = \sqrt{ {{( x_{2} - x_{1} ) }^{2} +( y_{2} - y_{1} ) }^{2} } }} \: \:$

$\\ \implies {\bold{10 = \sqrt{ {{( 3 - x) }^{2} +( 2 - 7) }^{2} } }} \: \:$

$\\ \implies {\bold{10 = \sqrt{ {{( 3 - x) }^{2} +( - 5) }^{2} } }} \: \:$

• Now square on both sides –

$\\ \implies {\bold{(10)^{2} = { {{( 3 - x) }^{2} +( - 5) }^{2} } }} \: \:$

$\\ \implies {\bold{100 = { {{( 3 - x) }^{2} +25} } }} \: \:$

$\\ \implies {\bold{75 = { {{( 3 - x) }^{2} } } }} \: \:$

• Now take square root on both sides –

$\\ \implies {\bold{3 - x = \pm \sqrt{75} }} \: \:$

$\\ \implies {\bold{ - x = \pm \sqrt{75} - 3 }} \: \:$

$\\ \implies {\bold{ x = - \sqrt{75} + 3 \: \: , \: \: x = \sqrt{75} + 3}} \: \:$