Contents

- 1 Which construction is illustrated above a parallel line to a given line?
- 2 What must be true about the slopes of two perpendicular lines?
- 3 Which of the following is true for perpendicular lines?
- 4 Is the line through points P (- 7 2 and Q?
- 5 What is the shortest segment from a point to a line?
- 6 Do parallel lines have the same slope?
- 7 What is the purpose of slope?
- 8 How do you know if a line is parallel?
- 9 What are two lines that intersect to form right angles called?
- 10 Do perpendicular lines form right angles?
- 11 Which best explains the relationship between lines A and B?
- 12 Is P 8/10 a line through a point?
- 13 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?
- 14 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?

## 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.

## 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**.

## 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.