Geometric Transformations and Properties

This video tutorial covers key eighth-grade math topics, including rational and irrational numbers, solving multi-step equations, understanding linear relationships and slope, exploring transformations and similar figures, and learning about angle relationships and the Pythagorean theorem. The tutorial provides methods for estimating irrational square roots, solving equations with variables on both sides, and graphing linear equations. It also explains transformations like rotations, reflections, and dilations, and discusses angle relationships and the Pythagorean theorem.

Which of the following is an example of an irrational number?

• √2

• 4

• 3.14

• 1/2

What is the first step in solving a multi-step equation with variables on both sides?

• Add the larger variable to both sides

• Subtract the smaller variable from both sides

• Divide both sides by the variable

• Multiply both sides by the variable

What is the term used to describe the slope of a vertical line?

• Undefined slope

• Positive slope

• Zero slope

• Negative slope

How do you find the slope of a line given two points?

• Divide the difference of y-coordinates by the difference of x-coordinates

• Add the x-coordinates

• Subtract the y-coordinates

• Multiply the x and y coordinates

When performing a 90-degree clockwise rotation, what happens to the coordinates of a point?

• The x coordinate becomes negative

• The y coordinate becomes negative

• The x and y coordinates are swapped

• Both coordinates remain the same

What type of transformation results in a figure that is similar but not congruent?

• Dilation

• Rotation

• Reflection

• Translation

What is the result when you reflect a point over the line y = 2?

• The y-coordinate changes

• The x-coordinate changes

• Both coordinates change

• Neither coordinate changes

If two angles are both acute and formed by a transversal line, what can be said about them?

• They are different

• They are equal

• They are complementary

• They are supplementary

What is the sum of the interior angles of a triangle?

• 270 degrees

• 360 degrees

• 180 degrees

• 90 degrees

In the Pythagorean theorem, what does 'c' represent?

• The longest side

• The shortest side

• Any side

• The middle side