Question

What is the distance between the points (2, 1) and (14, 6) on a coordinate
plane?

Answer 1

On a coordinate plane the distance is 13 units between the two points.

Explanation:

Given :

• (2, 1) and (14, 6)

Find the Distance

Solution:

• Applying Distance formulae,

`\rm \: D= \sqrt{(x_2 -x_1) {}^(2) +x_2 - x_1) {}^(2) }`

• 
  `(y_2,y_1) = (6,1)`
• 
  `(x_2,x_1) = (14,2)`

Solving,

• 
  `D = \sqrt{(14 - 2) { }^(2) + (6 - 1 ){}^(2) }`
• 
  `D= \sqrt{12 {}^(2) + 5 {}^(2) }`
• 
  `D = √(144 + 25)`
• 
  `D = √(169)`
• 
  `D = √(13 * 13)`
• 
  `D= 13`

So distance is 13.

Answer 2

d = 13 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 ) = (2, 1 ) and (x₂, y₂ ) = (14, 6 )

d =
`√((14-2)^2+(6-1)^2)`

=
`√(12^2+5^2)`

=
`√(144+25)`

=
`√(169)`

= 13