Question

Find the distance between M(7, 8) and N(-3,-8)

Answer 1

√356; around 18.86796 or 18.9

Answer 2

The distance between M(7, 8) and N(-3,-8) is 18.87.

Step-by-step Step-by-step explanation:

Solution :

Here's the required formula to find distance:

`\star{\underline{\boxed{\sf{\pink{\sqrt{\Big({x_(2) - x_(1) \Big)}^(2) + {\Big(y_(2) - y_(1) \Big)}^(2)}}}}}}`

• 
  `\rm{ x_2}` = -3
• 
  `\rm{ x_1}` = 7
• 
  `\rm{ y_2}` = -8
• 
  `\rm{ y_1}` = 8

Substituting all the given values in the formula to find distance :

`{\implies{\sf{Distance = \sqrt{\Big({x_(2) - x_(1) \Big)}^(2) + {\Big(y_(2) - y_(1) \Big)}^(2)}}}}`

`{\implies{\sf{Distance = \sqrt{\Big((- 3) -( 7) \Big)^(2) + \Big(( - 8 )-( 8) \Big)^(2)}}}}`

`{\implies{\sf{Distance = \sqrt{\Big( - 10\Big)^(2) + \Big( - 16\Big)^(2)}}}}`

`{\implies{\sf{Distance = √(\Big( - 10 * - 10\Big) + \Big( - 16 * - 16\Big))}}}`

`{\implies{\sf{Distance = √(\Big(100\Big) + \Big(256\Big))}}}`

`{\implies{\sf{Distance = √(100+ 256)}}}`

`{\implies{\sf{Distance = √(356)}}}`

`{\implies{\sf{Distance =18.87}}}`

`\star{\underline{\boxed{\sf{\pink{Distance = 18.87 \: units}}}}}`

Hence, the distance between M(7, 8) and N(-3,-8) is 18.87.

`\rule{300}{2.5}`