Geometry EOC Review: Key Concepts and Problem Solving

This video tutorial covers geometry transformations, including mapping figures, transformation rules, and coordinate transformations. It provides examples and problem-solving techniques, explains weighted averages, and discusses classifying shapes using coordinate geometry. The video concludes with a summary of key concepts.

What transformation maps a point (x, y) to (-x, -y)?

• Translation to the left by x units

• Rotation of 180 degrees about the origin

• Reflection over the x-axis

• Reflection over the y-axis

Which sequence correctly describes the transformation from triangle ABC to triangle DEF?

• Reflection over the x-axis followed by a reflection over the y-axis

• Translation down by 6 units

• Rotation of 180 degrees about the origin

• Rotation of 90 degrees clockwise

What is the result of rotating a figure 90 degrees clockwise around the origin?

• Both coordinates switch places

• The x-coordinate becomes the negative y-coordinate

• The y-coordinate becomes the negative x-coordinate

• The figure remains unchanged

Which transformation does not necessarily preserve the congruence of a geometric figure?

• Reflection across a line

• Rotation by any angle around a point

• Translation by any vector

• Scaling by a factor not equal to one

In a dilation transformation with a scale factor of 5, what happens to a point (x, y)?

• Its coordinates become (x/5, y/5)

• It moves 5 units closer to the origin

• Its coordinates become (5x, 5y)

• It moves 5 units away from the origin

What is the result of stretching point K by a factor of five in the direction from point J?

• K' coordinates are (32, 18)

• K' coordinates are (27, 28)

• K' coordinates are (35, 20)

• K' coordinates are (20, 30)

How do you calculate the weighted average of points on a line?

• Multiply each point's coordinate by its weight and sum the results

• Add all point coordinates and divide by the number of points

• None of the above

• Subtract the weighted coordinates from each other

What type of triangle is formed by vertices D, E, and F if two sides measure the same?

• Right triangle

• Isosceles

• Equilateral

• Scalene

Which statement is true when classifying a quadrilateral as a rectangle using coordinate geometry?

• Opposite sides are parallel and all angles are right angles

• All sides are of equal length

• Only one pair of opposite sides needs to be parallel

• Diagonals are perpendicular

What are the correct coordinates for point D to form a square with points A, B, and C?

• (7, 8)

• (8, 7)

• (9, 6)

• (6, 9)