Question

What expression gives the distance between the points (4,6) and (7,-3)?

Answer 1

By the distance formula,

`d = \sqrt{( x_2 - x_1) {}^(2) + (y_2 - y_1 {)}^(2) }`

Here,

`x_1 = 4`

`y_1 = 6`

`x_2 = 7`

`y_2 = - 3`

Hence,

`d = \sqrt{( {7 - 4)}^(2) + {( - 3 - 6)}^(2) }`

`d = \sqrt{ {3}^(2) + ( - {9)}^(2) }`

`d = √(9 + 81)`

`d = √(90)`

Answer 2

`√((-3^2-6)+(7^2-4^2))`

Explanation:

Use the form:
`\sqrt{(x^2-x^1)+(y2-y1)^2`

so:
`√((-3^2-6)+(7^2-4^2))`