To determine which ordered pairs could lie on a line that is perpendicular to a line with a slope of [tex]\(-\frac{4}{5}\)[/tex], we need to find the slope of the perpendicular line. The slope of a line perpendicular to another is the negative reciprocal of the slope of the original line.
1. Find the slope of the perpendicular line:
- The slope of the original line is [tex]\(-\frac{4}{5}\)[/tex].
- The negative reciprocal of [tex]\(-\frac{4}{5}\)[/tex] is [tex]\(\frac{5}{4}\)[/tex].
Therefore, the slope of the perpendicular line is [tex]\(\frac{5}{4}\)[/tex].
2. Calculate the slopes for the given pairs and check if they match [tex]\(\frac{5}{4}\)[/tex]:
- For the ordered pairs [tex]\((-2,0)\)[/tex] and [tex]\((2,5)\)[/tex]:
[tex]\[
\text{slope} = \frac{5 - 0}{2 - (-2)} = \frac{5}{4}
\][/tex]
This slope is [tex]\(\frac{5}{4}\)[/tex], so this pair satisfies the perpendicular condition.
- For the ordered pairs [tex]\((-4,5)\)[/tex] and [tex]\((4,-5)\)[/tex]:
[tex]\[
\text{slope} = \frac{-5 - 5}{4 - (-4)} = \frac{-10}{8} = -\frac{5}{4}
\][/tex]
This slope is [tex]\(-\frac{5}{4}\)[/tex], which does not satisfy the perpendicular condition.
- For the ordered pairs [tex]\((-3,4)\)[/tex] and [tex]\((2,0)\)[/tex]:
[tex]\[
\text{slope} = \frac{0 - 4}{2 - (-3)} = \frac{-4}{5}
\][/tex]
This slope is [tex]\(-\frac{4}{5}\)[/tex], which does not satisfy the perpendicular condition.
- For the ordered pairs [tex]\((1,-1)\)[/tex] and [tex]\((6,-5)\)[/tex]:
[tex]\[
\text{slope} = \frac{-5 - (-1)}{6 - 1} = \frac{-4}{5}
\][/tex]
This slope is [tex]\(-\frac{4}{5}\)[/tex], which does not satisfy the perpendicular condition.
- For the ordered pairs [tex]\((2,-1)\)[/tex] and [tex]\((10,9)\)[/tex]:
[tex]\[
\text{slope} = \frac{9 - (-1)}{10 - 2} = \frac{10}{8} = \frac{5}{4}
\][/tex]
This slope is [tex]\(\frac{5}{4}\)[/tex], so this pair satisfies the perpendicular condition.
3. Conclusion:
The ordered pairs that could lie on a line perpendicular to the one with a slope of [tex]\(-\frac{4}{5}\)[/tex] are:
[tex]\( \boxed{(-2,0) \text{ and } (2,5)} \)[/tex]
[tex]\( \boxed{(2,-1) \text{ and } (10,9)} \)[/tex]
