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Chapter 8: Problem 87

Answer true or false. A vertical line is always perpendicular to a horizontal line.

Short Answer

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True

Step by step solution

01

Understanding the terms

First, recall that a vertical line is a straight line that goes up and down, like the y-axis on a graph. A horizontal line, on the other hand, is a straight line that goes left to right, like the x-axis on a graph.
02

Definition of Perpendicular

Two lines are perpendicular if they intersect at a right angle (90 degrees). This means that the angle formed between them is a right angle.
03

Interaction of Vertical and Horizontal Lines

Consider a vertical line intersecting with a horizontal line. The meeting point creates four angles, each measuring 90 degrees. This means that when a vertical line intersects a horizontal line, they are always perpendicular to each other.
04

Conclusion

Since a vertical line always forms a right angle with a horizontal line when they intersect, the statement that a vertical line is always perpendicular to a horizontal line is true.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vertical Line
A vertical line is an essential concept in geometry and is pretty straightforward to understand. Imagine a straight line that runs up and down.
  • It is often associated with the y-axis of a graph.
  • Vertical lines appear to rise directly towards the sky or dip straight towards the ground.
A handy trick to remember how vertical lines work is to think of a tall building or a pole, both standing directly perpendicular to the ground they rest upon. Vertical lines can run through any point on the graph but will maintain the same direction鈥攕traight across the y-axis with no slant, giving it a rise but no run.
Horizontal Line
Much like its vertical counterpart, a horizontal line follows a straightforward path as well. Envision a straight line that stretches left to right.
  • It is associated with the x-axis on a graph.
  • Horizontal lines resemble horizons in landscapes or desks we use.
Unlike vertical lines, horizontal lines run flat with no rise over a given distance, stretching parallel to the x-axis and keeping a consistent level with zero rise. Remember, much like the horizon you see at the beach, a horizontal line gives a sense of calm uniformity as it doesn't dip or rise like its vertical friend.
Intersection
The intersection of two lines is a fascinating event in geometry. When two lines, no matter their types, cross paths, they create a point known as an intersection.
  • This is where two lines meet or cross over each other.
  • Intersections can create various angles, but with perpendicular lines, this would be a right angle.
Understanding intersections involves recognizing the point of meeting between lines, like road junctions that you might encounter during driving, which regulate traffic flow. In geometry, intersections help develop new angles and points, taking initial lines and forming new mathematical relationships from them.
Right Angle
A right angle is quite a remarkable aspect of geometry, characterized by a sharp, square-like angle measuring exactly 90 degrees.
  • It is the hallmark of perpendicular lines intersecting.
  • Shapes like squares and rectangles feature numerous right angles.
Spotting a right angle is simple with objects like books or smartphone corners exhibiting this precision. When perpendicular (vertical and horizontal) lines meet, they create these distinct right angles, ensuring balanced and uniform shapes in geometric designs and engineering applications. Think of right angles as nature's method of maintaining balance and symmetry, akin to the edges of structures.

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Most popular questions from this chapter

Solve. See the Concept Check in this section. Choose the type of variation that each equation represents. a Direct variation b. Inverse variation c. Joint variation $$ x y=\frac{2}{11} $$

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Write an equation to describe each variation. Use \(k\) for the constant of proportionality. See Examples I through \(7 .\) \(y\) varies directly as \(a^{5}\) and inversely as \(b\)
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