Respuesta :
Statements 2) Line SW has an undefined slope, 3)Line TV has a slope of 0, and 4) Lines RS and TV are parallel are correct.
It is given that there are three lines RS, TV, and SW.
Line RS goes through (-8, 6) and (2, 6).
Line TV goes through (-6, -4) and (8, -4).
Line SW goes through (2, 6) and (2,-8).
It is required to find true statements.
Statements are:
- 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.
What is a straight line?
A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]m=\frac{y_{2}-y_{1}}{{x_{2}-x_{1}}}[/tex]
Where [tex](x_{1}, y_{1}) and (x_{2}, y_{2})[/tex] are points lie on the line.
1. Finding line RS slope by using the above formula:
[tex]m=\frac{6-6}{2-(-8)}[/tex]
[tex]m=0[/tex]
2. similarly finding line SW slope:
[tex]m=[/tex] ∞
3. similarly finding line TV slope:
[tex]m=0[/tex]
4. If the two lines are parallel then their slope will be equal.
The slope of RS = The slope of TV.
Hence RS and TV are parallel.
5. If two lines are perpendicular then their product of slope will be -1.
Here we can see the product of the slope of SW and RS is not defined.
Hence these two lines aren't perpendicular.
Therefore, statements 2, 3, and 4 are correct.
Learn more about the slope of the straight line.
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