Question

Find the distance between (2,3) (4, -7)

Find the distance between (-9,-4) (-3,6)

Answer 1

Distance between (2 , 3) (4 , -7)

`d=\sqrt{(y_(2) -y_(1) )^(2) + (x_(2)-x_(1) )^(2)`

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

`d=\sqrt{(-10 )^(2) + (2 )^(2)`

`d=\sqrt{100 + 4`

`d=\sqrt{104`

`d=10.198` or
`2√(26)`

Answer 2

See below

Explanation:

To find the distance between two points, we use the distance formula:

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

(2, 3) and (4, -7)

Plug in what you know.

`d = √((4-2)^2 + (-7 - 3)^2 )`

Simplify the parentheses.

`d = √((2)^2 + (-10)^2 )`

Evaluate the exponents.

`d = √((4) + (100))`

Evaluate under the radical.

`d = √((104))`

Evaluate the square root.

`d = 10.198`

10.198 units

(-9, -4) and (-3, 6)

Plug in what you know.

`d = √((-3 -(-9))^2 + (6 - (-4))^2 )`

Simplify the parentheses.

`d = √((-3 + 9)^2 + (6 + 4)^2 )`

Simplify the parentheses.

`d = √((6)^2 + (10)^2 )`

Evaluate the exponents.

`d = √((36) + (100) )`

Evaluate under the radical.

`d = √((136))`

Evaluate the square root.

`d = 11.662`

11.662 units