Respuesta :
The correct answer is:
RS is perpendicular to MN and PQ.
Explanation:
We can use the slopes of these lines to determine the answer.
Slope is given by the formula
m=[tex] \frac{y_{2}- y_{1} }{ x_{2} - x_{1} } [/tex].
Using the coordinates for M and N, we have:
m=[tex] \frac{3--1}{3--3} = \frac{4}{6} = \frac{2}{3} [/tex].
Since PQ is parallel to MN, its slope will be [tex] \frac{2}{3} [/tex] as well, since parallel lines have the same slope.
Using the coordinates for points T and V in the slope formula, we have
m=[tex] \frac{-4-1}{0--4} =- \frac{5}{4} [/tex].
This is not parallel to MN or PQ, since the slopes are not the same.
We can also say that it is not perpendicular to these lines; perpendicular lines have slopes that are negative reciprocals (they are opposite signs and are flipped). This is not true of TV either.
Using the coordinates for R and S in the slope formula, we have
m=[tex] \frac{-2-1}{2-0} =- \frac{3}{2} [/tex]. Comparing this to the slope of RS, it is flipped and the sign is opposite; they are negative reciprocals, so they are perpendicular.
RS is perpendicular to MN and PQ.
Explanation:
We can use the slopes of these lines to determine the answer.
Slope is given by the formula
m=[tex] \frac{y_{2}- y_{1} }{ x_{2} - x_{1} } [/tex].
Using the coordinates for M and N, we have:
m=[tex] \frac{3--1}{3--3} = \frac{4}{6} = \frac{2}{3} [/tex].
Since PQ is parallel to MN, its slope will be [tex] \frac{2}{3} [/tex] as well, since parallel lines have the same slope.
Using the coordinates for points T and V in the slope formula, we have
m=[tex] \frac{-4-1}{0--4} =- \frac{5}{4} [/tex].
This is not parallel to MN or PQ, since the slopes are not the same.
We can also say that it is not perpendicular to these lines; perpendicular lines have slopes that are negative reciprocals (they are opposite signs and are flipped). This is not true of TV either.
Using the coordinates for R and S in the slope formula, we have
m=[tex] \frac{-2-1}{2-0} =- \frac{3}{2} [/tex]. Comparing this to the slope of RS, it is flipped and the sign is opposite; they are negative reciprocals, so they are perpendicular.
The slope of the line suggest the steepness and the direction of the line. The option a, c and e is correct.
Slope of the given line has to be find out.
What is slope of the line?
The slope of the line suggest the steepness and the direction of the line. The slope of a line having point [tex](x_1, x_2)[/tex] and [tex](y_1, y_2)[/tex] can be given as,
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Given information-
Lines MN and PQ are parallel.
Lines RS and TV intersect the lines MN and PQ.
- a) The slope of the line MN is,
[tex]m=\dfrac{3-(-1)}{3-(-3)} \\m=\dfrac{4}{6} \\m=\dfrac{2}{3}[/tex]
Thus the slope of the line MN is 2/3.
Hence option a is correct.
- b) The slope of line PQ is undefined -As the lines MN and PQ are parallel. The parallel line has equal slope. Thus the slope of PQ is 2/3. Hence option b is incorrect.
- c) The slope of the line RS is-
[tex]m=\dfrac{-2-(-1)}{2-0} \\m=\dfrac{-3}{2}[/tex]
Thus the slope of the line RS is -3/2.
Hence option c is correct.
- d) Lines RS and TV are parallel-the slope of line TV,
[tex]m=\dfrac{-4-(-1)}{0-(-4)} \\m=\dfrac{-5}{4}[/tex]
Thus the slope of the line TV is -5/4.
- As the slope of RS and TV is not equal thus the line RS and TV is not parallel.
Hence option d is incorrect.
- e) Line RS is perpendicular to both line MN and line PQ-Perpendicular lines has inverse and opposite slope. The slope of the line RS is perpendicular to both line MN and line PQ as the slope of it is inverse and opposite to line MN and line PQ.
Hence the option e is correct.
Hence the option a, c and e is correct.
Learn more about the slope of the line here;
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