Question

Find length between AC-3,8) and B(5,-4) in simplest radical form:

Answer 1

The Points are in the form (x,y), and they are A(-3,8) and B(5,-4).

The length between two points is:

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

In this case:

`\text{length = }\sqrt[]{(-3-5)^2+(8-(-4))^2}=\sqrt[]{(-8)^2+(12)^2}=\sqrt[]{64+144}`
`\text{length =}\sqrt[]{208}\text{ = }\sqrt[]{16\cdot13}=4\sqrt[]{13}`

The correct anser is:

`\text{length = 4}\sqrt[]{13}`