Question

Find the distance when y2=9, y1=13, x2=4, and x1=0.

Answer 1

Tthe distance between
`\left(x_1,\:y_1\right)=\left(0,\:13\right)` and
`\left(x_2,\:y_2\right)=\left(4,\:9\right)` will be:

• 
  `\mathrm{Distance\:between\:}\left(0,\:13\right)\mathrm{\:and\:}\left(4,\:9\right):\quad 4√(2)`

Explanation:

Given the points

• 
  `\left(x_1,\:y_1\right)=\left(0,\:13\right)`

• 
  `\left(x_2,\:y_2\right)=\left(4,\:9\right)`

`\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad √(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

`\mathrm{The\:distance\:between\:}\left(0,\:13\right)\mathrm{\:and\:}\left(4,\:9\right)\mathrm{\:is\:}`

`=√(\left(4-0\right)^2+\left(9-13\right)^2)`

`=√(4^2+4^2)`

`=√(4^2\cdot \:2)`

`\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0`

`=√(2)√(4^2)`

`\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0`

`=4√(2)`

Therefore, the distance between
`\left(x_1,\:y_1\right)=\left(0,\:13\right)` and
`\left(x_2,\:y_2\right)=\left(4,\:9\right)` will be:

• 
  `\mathrm{Distance\:between\:}\left(0,\:13\right)\mathrm{\:and\:}\left(4,\:9\right):\quad 4√(2)`