Perpendicular lines
Perpendicular lines is a skill on Pengi from Lesson 5: Properties of Lines in Yoshiwara Elementary Algebra.
Key Concepts
Property Two lines are perpendicular if the product of their slopes is $ 1$, that is, if $$m 1 m 2 = 1$$ or if one of the lines is horizontal and one is vertical. The slope of one perpendicular line is the negative reciprocal of the other: $$m 2 = \frac{ 1}{m 1}$$.
Examples A line with slope $m 1 = 5$ is perpendicular to a line with slope $m 2 = \frac{1}{5}$ because their product is $5 \times ( \frac{1}{5}) = 1$. The lines $y = \frac{3}{4}x + 2$ and $y = \frac{4}{3}x 1$ are perpendicular. Their slopes are $m 1 = \frac{3}{4}$ and $m 2 = \frac{4}{3}$, and their product is $(\frac{3}{4})( \frac{4}{3}) = 1$. The line $y = 5$ is horizontal (slope is 0), and the line $x = 1$ is vertical (slope is undefined). These lines are perpendicular.
Explanation Perpendicular lines intersect at a perfect right angle, like the corner of a book. Their slopes are opposites in two ways: one is positive while the other is negative, and their fractions are flipped (reciprocals).
Common Questions
What is Perpendicular lines?
Perpendicular lines is a skill on Pengi from Lesson 5: Properties of Lines in Yoshiwara Elementary Algebra.
What grade level is Perpendicular lines for?
Perpendicular lines is part of the Grade 6 Math curriculum, covered in Yoshiwara Elementary Algebra. It is designed for students studying Math at the Grade 6 level.
How can I learn Perpendicular lines?
Pengi offers an AI-guided lesson for Perpendicular lines that walks you through the key concepts step by step. The lesson is aligned to Yoshiwara Elementary Algebra so the content matches what you see in class.
How do I practice Perpendicular lines?
After learning the concept, use the Practice mode to work through targeted exercises on Perpendicular lines. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Perpendicular lines?
Perpendicular lines is covered in Yoshiwara Elementary Algebra, specifically in Chapter 3: Graphs of Linear Equations under Lesson 5: Properties of Lines. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Perpendicular lines free to study on Pengi?
Yes, the core Learn and Practice modes for Perpendicular lines are available for free on Pengi. No credit card is required to start studying.