Question
Lines RS, TV, and SW are shown.
On a coordinate plane, 3 lines are shown. Line R S goes through (negative 8, 6) and (2, 6). Line T V goes through (negative 6, negative 4) and (8, negative 4). Line S W goes through (2, 6) and (2, negative 8).
Which statements are true about these lines? Select three options.
Line RS has a slope of 6.
Line SW has an undefined slope.
Line TV has a slope of 0.
Lines RS and TV are parallel.
Line SW is perpendicular to line RS, but not to line TV.
On a coordinate plane, 3 lines are shown. Line R S goes through (negative 8, 6) and (2, 6). Line T V goes through (negative 6, negative 4) and (8, negative 4). Line S W goes through (2, 6) and (2, negative 8).
Which statements are true about these lines? Select three options.
Line RS has a slope of 6.
Line SW has an undefined slope.
Line TV has a slope of 0.
Lines RS and TV are parallel.
Line SW is perpendicular to line RS, but not to line TV.
Answers
GPT-4o mini
To analyze the lines RS, TV, and SW based on the given coordinates and determine which statements are true, let's go through each statement:
1. **Line RS has a slope of 6.**
- Line RS passes through points (−8, 6) and (2, 6). The y-coordinates are constant (6), so the slope \( m \) can be calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 6}{2 - (-8)} = \frac{0}{10} = 0
\]
- **This statement is false.**
2. **Line SW has an undefined slope.**
- Line SW passes through points (2, 6) and (2, −8). The x-coordinates are constant (2), so the slope is undefined because:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-8 - 6}{2 - 2} = \frac{-14}{0}
\]
- **This statement is true.**
3. **Line TV has a slope of 0.**
- Line TV passes through points (−6, −4) and (8, −4). The y-coordinates are constant (−4), so the slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - (-4)}{8 - (-6)} = \frac{0}{14} = 0
\]
- **This statement is true.**
4. **Lines RS and TV are parallel.**
- Line RS has a slope of 0 (as calculated), and Line TV also has a slope of 0. Since they have the same slope, they are parallel.
- **This statement is true.**
5. **Line SW is perpendicular to line RS, but not to line TV.**
- Line RS has a slope of 0 and line SW has an undefined slope. A vertical line (undefined slope) is perpendicular to a horizontal line (slope of 0). Therefore, line SW is perpendicular to line RS.
- Line SW is not perpendicular to line TV since line TV also has a slope of 0.
- **This statement is true.**
### Summary of True Statements:
- Line SW has an undefined slope.
- Line TV has a slope of 0.
- Lines RS and TV are parallel.
- Line SW is perpendicular to line RS, but not to line TV.
Thus, the three statements that are true are:
1. Line SW has an undefined slope.
2. Line TV has a slope of 0.
3. Lines RS and TV are parallel.
1. **Line RS has a slope of 6.**
- Line RS passes through points (−8, 6) and (2, 6). The y-coordinates are constant (6), so the slope \( m \) can be calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 6}{2 - (-8)} = \frac{0}{10} = 0
\]
- **This statement is false.**
2. **Line SW has an undefined slope.**
- Line SW passes through points (2, 6) and (2, −8). The x-coordinates are constant (2), so the slope is undefined because:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-8 - 6}{2 - 2} = \frac{-14}{0}
\]
- **This statement is true.**
3. **Line TV has a slope of 0.**
- Line TV passes through points (−6, −4) and (8, −4). The y-coordinates are constant (−4), so the slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - (-4)}{8 - (-6)} = \frac{0}{14} = 0
\]
- **This statement is true.**
4. **Lines RS and TV are parallel.**
- Line RS has a slope of 0 (as calculated), and Line TV also has a slope of 0. Since they have the same slope, they are parallel.
- **This statement is true.**
5. **Line SW is perpendicular to line RS, but not to line TV.**
- Line RS has a slope of 0 and line SW has an undefined slope. A vertical line (undefined slope) is perpendicular to a horizontal line (slope of 0). Therefore, line SW is perpendicular to line RS.
- Line SW is not perpendicular to line TV since line TV also has a slope of 0.
- **This statement is true.**
### Summary of True Statements:
- Line SW has an undefined slope.
- Line TV has a slope of 0.
- Lines RS and TV are parallel.
- Line SW is perpendicular to line RS, but not to line TV.
Thus, the three statements that are true are:
1. Line SW has an undefined slope.
2. Line TV has a slope of 0.
3. Lines RS and TV are parallel.