To find which ordered pairs could be points on a line that is perpendicular to a line with slope [tex]\(-\frac{4}{5}\)[/tex], we need to find the slope of the perpendicular line first. The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope.
Given slope of the original line:
[tex]\[ m = -\frac{4}{5} \][/tex]
The slope of the perpendicular line (let's denote it as [tex]\( m_p \)[/tex]) is:
[tex]\[ m_p = \frac{5}{4} \][/tex]
Now, let's check each pair of points to see if they form a line with slope [tex]\(\frac{5}{4}\)[/tex].
### 1. Pair: [tex]\((-2, 0)\)[/tex] and [tex]\((2, 5)\)[/tex]
Calculate the slope:
[tex]\[
\text{slope} = \frac{5 - 0}{2 - (-2)} = \frac{5}{4}
\][/tex]
This pair has the correct slope of [tex]\(\frac{5}{4}\)[/tex].
### 2. Pair: [tex]\((-4, 5)\)[/tex] and [tex]\((4, -5)\)[/tex]
Calculate the slope:
[tex]\[
\text{slope} = \frac{-5 - 5}{4 - (-4)} = \frac{-10}{8} = -\frac{5}{4}
\][/tex]
This pair does not have the correct slope. It is not perpendicular.
### 3. Pair: [tex]\((-3, 4)\)[/tex] and [tex]\((2, 0)\)[/tex]
Calculate the slope:
[tex]\[
\text{slope} = \frac{0 - 4}{2 - (-3)} = \frac{-4}{5}
\][/tex]
This pair does not have the correct slope. It is not perpendicular.
### 4. Pair: [tex]\((1, -1)\)[/tex] and [tex]\((6, -5)\)[/tex]
Calculate the slope:
[tex]\[
\text{slope} = \frac{-5 - (-1)}{6 - 1} = \frac{-4}{5}
\][/tex]
This pair does not have the correct slope. It is not perpendicular.
### 5. Pair: [tex]\((2, -1)\)[/tex] and [tex]\((10, 9)\)[/tex]
Calculate the slope:
[tex]\[
\text{slope} = \frac{9 - (-1)}{10 - 2} = \frac{10}{8} = \frac{5}{4}
\][/tex]
This pair has the correct slope of [tex]\(\frac{5}{4}\)[/tex].
### Conclusion
The two pairs of points that form a line perpendicular to the given line are:
- [tex]\((-2, 0)\)[/tex] and [tex]\((2, 5)\)[/tex]
- [tex]\((2, -1)\)[/tex] and [tex]\((10, 9)\)[/tex]
