To determine which ordered pairs could be points on a line perpendicular to a line with a slope of \(-\frac{4}{5}\), we first need to find the slope of a line that is perpendicular to it.
The product of the slopes of two perpendicular lines is \(-1\). If one slope is \(-\frac{4}{5}\), the perpendicular slope \(m\) can be found as follows:
\[ m \cdot -\frac{4}{5} = -1 \]
Solving for \(m\):
\[ m = \frac{5}{4} \]
Now, the lines that we are checking must have a slope of \(\frac{5}{4}\) in order to be perpendicular to the original line.
We will calculate the slope for the pairs of points given, and see if any pair has a slope of \(\frac{5}{4}\):
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For (–2, 0) and (2, 5): \[ \text{slope} = \frac{5 - 0}{2 - (-2)} = \frac{5}{4} \]
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For (–4, 5) and (4, –5): \[ \text{slope} = \frac{-5 - 5}{4 - (-4)} = \frac{-10}{8} = -\frac{5}{4} \]
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For (–3, 4) and (2, 0): \[ \text{slope} = \frac{0 - 4}{2 - (-3)} = \frac{-4}{5} \]
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For (1, –1) and (6, –5): \[ \text{slope} = \frac{-5 - (-1)}{6 - 1} = \frac{-4}{5} \]
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For (2, –1) and (10, 9): \[ \text{slope} = \frac{9 - (-1)}{10 - 2} = \frac{10}{8} = \frac{5}{4} \]
From the calculations above, we can see that the pairs of points that produce a slope of \(\frac{5}{4}\) are:
- (–2, 0) and (2, 5)
- (2, –1) and (10, 9)
Thus, the two correct options for ordered pairs that could be points on a line that is perpendicular to the original line with slope \(-\frac{4}{5}\) are:
(–2, 0) and (2, 5)
(2, –1) and (10, 9)
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