Question

What point on the number line is three fifths of the way from the point ?3 to the point 3? 0.6 ?0.6 1 ?1

Answer 1

So, the point three-fifths of the way from
`\(-3\) to \(3\) is \((3)/(5)\)` on the number line.

To find a point that is three-fifths of the way from
`\(-3\) to \(3\)`, you can use the following formula:

`\[ \text{Midpoint} = (a + b)/(2) \]`

In this case,
`\(a\)` is the starting point
`(\(-3\))`,
`\(b\)` is the ending point
`(\(3\))`, and we want a point that is three-fifths of the way from
`\(a\) to \(b\)`. The formula becomes:

`\[ \text{Point} = a + (3)/(5)(b - a) \]`

Substitute the values:

`\[ \text{Point} = -3 + (3)/(5)(3 - (-3)) \]`

`\[ \text{Point} = -3 + (3)/(5)(6) \]`

`\[ \text{Point} = -3 + (18)/(5) \]`

To make the denominators the same:

`\[ \text{Point} = (-15)/(5) + (18)/(5) \]`

`\[ \text{Point} = (3)/(5) \]`