Question

Find the distance between the points (2, 1) and (9,0).

Give an exact answer in simplest radical form. Do not round.

Answer 1

5√2 units

Explanation:

Use distance formulae to find out the distance.

• 
  `\rm \: Distance = \sqrt{(x_2-x_1) {}^(2) +(y_2-y_1) {}^(2) }`

ATQ,

• 
  `\rm \: (x_2,x_1) = (9,2)`
• 
  `\rm (y_2,y_1) = (0,1)`

Substituting them on the formulae,we obtain

• 
  `\rm \: Distance \: D = \sqrt{(9 - 2) {}^(2) + (0 - 1) {}^(2) }`
• 
  `\rm \: Distance \: D = \sqrt{7 {}^(2) - 1 {}^(2) }`
• 
  `\rm \: Distance \; D = √(49 + (- 1 * - 1))`
• 
  `\rm Distance \: D = √(49 + 1)`
• 
  `\rm Distance\; D = √(50)`
• 
  `\boxed{ \rm \: Distance \: D = 5 √(2) \: units}`