Question

Find the distance between the points ( – 9, – 7) and ( – 3,1).

Answer 1

Given:-

• 
  `\textrm{( - 9, - 7)}`

`\:`

• 
  `\textrm{( -3 , 1 )}`

`\:`

To find:-

• 
  `\textrm{Distance between two points = ?}`

`\:`

By using formula:-

• 
  `\underline{ \star \small \boxed{{ \rm{ \purple{Distance = √(( x_2 - x_1 )² + ( y_2 - y_1 )²) }}}}}`

`\:`

Solution:-

• 
  `\rm \: D =√( ( x_2 - x_1 )² + ( y_2 - y_1 )²)`

`\:`

where ,

`\: \: \star \rm \red{x_1 = -9 , x_2 = -3 } \\\star \green {\rm y_1 = -7 , y_2 = 1}`

`\:`

• 
  `\rm \: D = √( ( -3 - ( - 9 ))² + ( 1 - (-7 ))²)`

`\:`

• 
  `\rm \: D = √(( -3 + 9)² + ( 1 + 7 )²)`

`\:`

• 
  `\rm \: D = √(( 6 )² + ( 8 )²)`

`\:`

• 
  `\rm \: D = √(36 + 64 )`

`\:`

• 
  `\rm \: D = √(100)`

`\:`

• 
  `\boxed{ \textrm{ \color{green}{D = 10 \: }}}`

`\:`

Therefore , the distance between two points is 10 units !

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙

Answer 2

10 units

Explanation:

calculate the distance d using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = (- 9, - 7 ) and (x₂, y₂ ) = (- 3, 1 )

d =
`√((-3-(-9))^2+(1-(-7)^2)`

=
`√((-3+9)^2+(1+7)^2)`

=
`√(6^2+8^2)`

=
`√(36+64)`

=
`√(100)`

= 10 units