Geometry and Probability Concepts

The video tutorial covers Lesson 2.1.3, focusing on solving systems of equations both graphically and algebraically using Desmos. It includes calculating the area of rectangles and understanding geometric assumptions. The lesson also explores angle relationships and probability, followed by reflections of line segments to form geometric shapes. The tutorial concludes with a summary and encourages viewers to ask questions in the comments.

What is the solution to the system of equations y = -x + 1 and y = 2x + 7?

• (-3, 2)

• (3, -2)

• (-2, 3)

• (2, -3)

How do you find the area of a rectangle with sides of 5 units and 4 units?

• Divide the sides

• Subtract the sides

• Multiply the sides

• Add the sides

What is the area of a rectangle with dimensions 104 units by 25 units?

• 2,400 units squared

• 2,500 units squared

• 2,700 units squared

• 2,600 units squared

What is necessary to assume two angles are equal in a geometric diagram?

• The angles are vertical

• The angles are adjacent

• The lines are parallel

• The lines are perpendicular

If two angles are corresponding in parallel lines, what can be said about them?

• They are alternate

• They are complementary

• They are supplementary

• They are equal

What is the probability of selecting a boy from a class if the probability is one third?

• 1/5

• 1/3

• 1/2

• 1/4

If there are 11 boys in a class, how many girls are there if the probability of selecting a boy is one third?

• 25

• 22

• 11

• 24

What shape is formed when a line segment is reflected across a line and connected to its original?

• Triangle

• Circle

• Square

• Rectangle

What is the result of reflecting a line segment across the line y = -x + 6?

• Square

• Triangle

• Rectangle

• Parallelogram

What is the relationship between the sides of a rectangle formed by reflection?

• All sides are equal

• Opposite sides are equal

• No sides are equal

• Adjacent sides are equal