Distance and Reflection in Geometry

This lesson covers the concept of distance in the coordinate plane, focusing on how to use absolute value to find distances between points with the same X or Y coordinates. It explains reflecting points across axes and the relationships between original points and their reflections. The lesson also includes methods for calculating distances between points and applies these concepts to real-world scenarios, such as determining travel time between locations.

What is the significance of using absolute value when calculating distance in the coordinate plane?

• It allows for negative distances.

• It is only used for vertical distances.

• It ensures the distance is always positive.

• It simplifies the calculation process.

When reflecting a point over the y-axis, what happens to the x-coordinate?

• It remains the same.

• It becomes the opposite sign.

• It doubles.

• It becomes zero.

If a point (3, -2) is reflected over the x-axis, what will be the new coordinates?

• (3, 2)

• (-3, -2)

• (3, -2)

• (-3, 2)

What is the relationship between the coordinates of a point and its reflection over both axes?

• Only the y-coordinate changes.

• Both coordinates change to their opposites.

• Only the x-coordinate changes.

• Both coordinates remain the same.

How do you find the distance between two points with the same y-coordinate?

• Calculate the midpoint.

• Count the vertical squares between them.

• Count the horizontal squares between them.

• Use the distance formula.

What is the distance between points E(-4, 3) and F(5, 3) on the coordinate plane?

• 11 units

• 5 units

• 9 units

• 7 units

If a truck travels at 40 miles per hour, how long will it take to cover a distance of 120 miles?

• 2 hours

• 3 hours

• 5 hours

• 4 hours

In a coordinate plane map where each grid represents 20 miles, how many miles are between two points that are 6 grids apart?

• 120 miles

• 100 miles

• 80 miles

• 60 miles

What is the travel time for a truck moving at 50 miles per hour over a distance of 40 miles?

• 1.2 hours

• 1 hour

• 0.8 hours

• 1.5 hours

How many minutes does it take to travel 40 miles at a speed of 50 miles per hour?

• 48 minutes

• 40 minutes

• 60 minutes

• 30 minutes