Question

Find the distance between (1, 0) and (9, 15).

Answer 1

`\mathrm{Distance\:between\:}\left(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)=\:17`

Explanation:

Given the points

• (1, 0)

• (9, 15)

`\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(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)\mathrm{\:is\:}`

`=√(\left(9-1\right)^2+\left(15-0\right)^2)`

`=√(8^2+\left(15-0\right)^2)`

`=√(8^2+15^2)`

`=√(64+225)`

`=√(289)`

`=√(17^2)`

`=17` ∵
`\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a`

Therefore,

`\mathrm{Distance\:between\:}\left(1,\:0\right)\mathrm{\:and\:}\left(9,\:15\right)=\:17`