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3 years ago

Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is −34?

Mathematics

1 answer:

Zigmanuir [339]3 years ago

8 0

Given:

The slope of a line is $-\dfrac{3}{4}$ .

To find:

The lines in the options are parallel, perpendicular or neither parallel nor perpendicular to the given line.

Solution:

We know that the slopes of parallel lines are equal.

The slope of line Q and the slope of given line are same, i.e., $-\dfrac{3}{4}$ . So, the line Q is parallel to the given line.

The slope of a perpendicular line is the opposite reciprocal of the slope of the line because the product of slopes of two perpendicular lines is -1.

The slope of a line is $-\dfrac{3}{4}$ . It means the slope of the perpendicular line must be $\dfrac{4}{3}$ . So, the line N is perpendicular to the given line.

The slopes of line M and P are neither equal to the slope of the given line nor opposite reciprocal of the slope of the line.

Therefore, the lines M and P are neither parallel nor perpendicular.

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Checking:

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Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

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