Question

What is the distance between (8,-4) and (3,8) in the simplest radical form

Answer 1

13

Explanation:

To find the distance we use the formula,

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

where, x₁ = 8, x₂ = 3 and y₁ = -4, y₂ = 8

`\sqrt{(3 - 8) {}^(2) + (8 - ( - 4) {}^(2) }`

`\sqrt{( - 5) {}^(2) + (12) {}^(2) }`

`√(25 + 144)`

`√(169)`

`13`

Therefore, the distance is 13 in simple radical form

Answer 2

Explanation:

To find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane, we can use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the points are (8, -4) and (3, 8). Plugging these values into the distance formula:

Distance = √((3 - 8)^2 + (8 - (-4))^2)

= √((-5)^2 + (8 + 4)^2)

= √(25 + 12^2)

= √(25 + 144)

= √169

= 13

Therefore, the distance between (8, -4) and (3, 8) is 13 in the simplest radical form.