Quick Answer: Which Construction Is Illustrated Above?

Which construction is illustrated above a parallel line to a given line?

Answer Expert Verified

The construction illustrated above is a parallel line to a given line from a point not on the line. Option (A) is correct. Explanation: From the figure it has been observed that the two line are parallel to each other.

What must be true about the slopes of two perpendicular lines?

Theorem 105: If two nonvertical lines are perpendicular, then their slopes are opposite reciprocals of one another, or the product of their slopes is −1. Horizontal and vertical lines are always perpendicular: therefore, two lines, one of which has a zero slope and the other an undefined slope are perpendicular.

Which of the following is true for perpendicular lines?

Explanation: The TRUE statement: “The lines intersect and are perpendicular.” This is true because the slopes of the two lines are opposite-reciprocals of each other. “The lines intersect at the point.” The lines actually intersect at the point.

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Is the line through points P (- 7 2 and Q?

Yes; The lines are both vertical.

What is the shortest segment from a point to a line?

The shortest segment from a point to a line is perpendicular to the line. This fact is used to define the distance from a point to a line as the length of the perpendicular segment from the point to the line.

Do parallel lines have the same slope?

As mentioned above, parallel lines have the same slope. So, if we know the slope of the line parallel to our line, we have it made.

What is the purpose of slope?

Slope measures the rate of change in the dependent variable as the independent variable changes. Mathematicians and economists often use the Greek capital letter D or D as the symbol for change. Slope shows the change in y or the change on the vertical axis versus the change in x or the change on the horizontal axis.

How do you know if a line is parallel?

We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.

What are two lines that intersect to form right angles called?

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Do perpendicular lines form right angles?

Recall that when two lines are perpendicular, they meet to form right angles.

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Which best explains the relationship between lines A and B?

Which best explains the relationship between lines a and b? They are skew and will never intersect. They are parallel and will never intersect. They are perpendicular and will intersect.

Is P 8/10 a line through a point?

Answer: No, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5). Step-by-step explanation: Two lines are called perpendicular to each other if the product of their slope is -1.

Is the line through points P 0 5 and Q 1/8 parallel to the line through points r 3 3 and S 5 1 )? Explain?

Is the line through points P(, 5) and Q(–1, 8) parallel to the line through points R(3, 3) and S(5, –1)? Explain. Yes, the lines have equal slopes.

Is the line through points P 3/5 and Q 1/4 parallel to the line through points r 1 1 and S 3 3 )? Explain?

Is the line through points P(3, –5) and Q(1, 4) parallel to the line through points R(–1, 1) and S(3, –3)? b Yes; the lines have equal slopes. c No; one line has zero slope, the other has no slope.

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