Question

What is the distance between P(12, 4) and Q(-8, 2)

Answer 1

Answer:
`2√(101)`

Explanation:

The distance between two points can be calculated with the following formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Given the points P(12, 4) and Q(-8, 2), we can identify that:

`x_2=-8\\x_1=12\\y_2=2\\y_1=4`

Then, substituing values into the formula, we get that the distance between these two points is:

`d_((PQ))=√((-8-12)^2+(2-4)^2)\\\\d_((PQ))=2√(101)`

Answer 2

`\huge{\boxed{2 √(101)}}`

The distance formula is
`√((x_2-x_1)^2+(y_2-y_1)^2)`, where
`(x_1, y_1)` and
`(x_2, y_2)` are the points.

Substitute in the points.
`√((2-4)^2+(-8-12)^2)`

Subtract.
`√((-2)^2+(-20)^2)`

Solve the exponents.
`√(4+400)`

Add.
`√(404)`

Now, we can simplify this square root just a little bit.
`404` has a square factor of
`4`.
`√(404)=√(4)*√(101)`

The square root of
`4` equals
`2`.
`\boxed{2 √(101)}`