Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is [tex]-\frac{3}{4}[/tex]?

Drag each choice into the boxes to correctly complete the table.

| Line | Slope | Relation to [tex]-\frac{3}{4}[/tex] |
|------|-----------------|-------------------------------------|
| [tex]$m$[/tex] | [tex]$\frac{3}{4}$[/tex] | |
| [tex]$n$[/tex] | [tex]$\frac{4}{3}$[/tex] | |
| [tex]$p$[/tex] | [tex]$-\frac{4}{3}$[/tex] | |
| [tex]$q$[/tex] | [tex]$-\frac{3}{4}$[/tex] | |

Choices:
- Parallel
- Perpendicular
- Neither

Sagot :

GinnyAnswer
To determine whether each line is parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is [tex]\(-\frac{3}{4}\)[/tex], we need to compare the slopes. Here are the steps and definitions we use:

1. Parallel Lines: Two lines are parallel if they have the same slope.
2. Perpendicular Lines: Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
3. Neither: If the lines are neither parallel nor perpendicular, they fall into this category.

Given slopes:
- Line [tex]\( m \)[/tex] with slope [tex]\(\frac{3}{4}\)[/tex]
- Line [tex]\( n \)[/tex] with slope [tex]\(\frac{4}{3}\)[/tex]
- Line [tex]\( p \)[/tex] with slope [tex]\(-\frac{4}{3}\)[/tex]
- Line [tex]\( q \)[/tex] with slope [tex]\(-\frac{3}{4}\)[/tex]

We compare each slope with the given slope [tex]\(-\frac{3}{4}\)[/tex]:

### Line [tex]\( m \)[/tex] with slope [tex]\(\frac{3}{4}\)[/tex]
- Parallel: [tex]\(\frac{3}{4} \ne -\frac{3}{4}\)[/tex]
- Perpendicular: [tex]\(\frac{3}{4} \times \left(-\frac{3}{4}\right) = -\frac{9}{16} \ne -1\)[/tex]
- Therefore, Line [tex]\( m \)[/tex] is Neither parallel nor perpendicular.

### Line [tex]\( n \)[/tex] with slope [tex]\(\frac{4}{3}\)[/tex]
- Parallel: [tex]\(\frac{4}{3} \ne -\frac{3}{4}\)[/tex]
- Perpendicular: [tex]\(\frac{4}{3} \times \left(-\frac{3}{4}\right) = -1\)[/tex]
- Therefore, Line [tex]\( n \)[/tex] is Perpendicular.

### Line [tex]\( p \)[/tex] with slope [tex]\(-\frac{4}{3}\)[/tex]
- Parallel: [tex]\(-\frac{4}{3} \ne -\frac{3}{4}\)[/tex]
- Perpendicular: [tex]\(-\frac{4}{3} \times \left(-\frac{3}{4}\right) = \frac{16}{9} \ne -1\)[/tex]
- Therefore, Line [tex]\( p \)[/tex] is Neither parallel nor perpendicular.

### Line [tex]\( q \)[/tex] with slope [tex]\(-\frac{3}{4}\)[/tex]
- Parallel: [tex]\(-\frac{3}{4} = -\frac{3}{4}\)[/tex]
- Therefore, Line [tex]\( q \)[/tex] is Parallel.

So, the completed table should be:

- Line [tex]\( m \)[/tex]: Neither
- Line [tex]\( n \)[/tex]: Perpendicular
- Line [tex]\( p \)[/tex]: Neither
- Line [tex]\( q \)[/tex]: Parallel
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.