Lines MN and PQ are parallel. Lines RS and TV intersect them. Which statements are true about these lines? Check all that apply.
The slope of line MN is .
The slope of line PQ is undefined.
The slope of line RS is .
Lines RS and TV are parallel.
Line RS is perpendicular to both line MN and line PQ.
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=\(\frac{y_{2}- y_{1} }{ x_{2} - x_{1} }\).
Using the coordinates for M and N, we have:
m=\(\frac{3--1}{3--3} = \frac{4}{6} = \frac{2}{3}\).
Since PQ is parallel to MN, its slope will be \(\frac{2}{3}\) as well, since parallel lines have the same slope.
Using the coordinates for points T and V in the slope formula, we have
m=\(\frac{-4-1}{0--4} =- \frac{5}{4}\).
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=\(\frac{-2-1}{2-0} =- \frac{3}{2}\). 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.
The slope of the line suggest the steepness and the direction of the line. The slope of a line having point \((x_1, x_2)\) and \((y_1, y_2)\) can be given as,
\(m=\dfrac{y_2-y_1}{x_2-x_1}\)
Given information-
Lines MN and PQ are parallel.
Lines RS and TV intersect the lines MN and PQ.
\(m=\dfrac{3-(-1)}{3-(-3)} \\m=\dfrac{4}{6} \\m=\dfrac{2}{3}\)
Thus the slope of the line MN is 2/3.
Hence option a is correct.
\(m=\dfrac{-2-(-1)}{2-0} \\m=\dfrac{-3}{2}\)
Thus the slope of the line RS is -3/2.
Hence option c is correct.
\(m=\dfrac{-4-(-1)}{0-(-4)} \\m=\dfrac{-5}{4}\)
Thus the slope of the line TV is -5/4.
Hence option d is incorrect.
Hence the option e is correct.
Hence the option a, c and e is correct.
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