Rectangle Properties and Geometry

The video tutorial covers lesson 19 on problem-solving in the coordinate plane. It begins with an opening exercise on finding the distance between points using absolute value. The exploratory challenge involves labeling and locating points, drawing line segments, and determining their lengths. The tutorial then focuses on constructing a rectangle, finding its vertices, and calculating its perimeter and area. The final exercise involves constructing a rectangle with specific criteria, ensuring each vertex lies in a different quadrant, and verifying the perimeter using absolute values.

What is the distance between the points (5, 4) and (5, -3) using absolute values?

• 7 units

• 8 units

• 9 units

• 10 units

How long is the line segment between the points (4, 5) and (4, -3)?

• 7 units

• 9 units

• 6 units

• 8 units

If a horizontal line segment starts at (4, -3) and is 9 units long, what is one possible endpoint?

• (4, 6)

• (13, -3)

• (4, -12)

• (-5, -3)

Why can't the point (13, -3) be graphed on the given grid?

• The y-coordinate is incorrect.

• The point is in the wrong quadrant.

• The point is not on the x-axis.

• The grid is not large enough.

What is the fourth vertex of a rectangle with vertices at (4, 5), (4, -3), and (-5, -3)?

• (-5, -5)

• (5, 5)

• (-5, 5)

• (5, -5)

How does the fourth vertex relate to the other vertices in a rectangle?

• It has the same x-value as the point above it.

• It has the same y-value as the point to the left.

• It has the same y-value as the point below it.

• It has the same x-value as the point below it.

What is the perimeter of a rectangle with a length of 8 units and a width of 9 units?

• 30 units

• 32 units

• 34 units

• 36 units

What is the area of a rectangle with a length of 8 units and a width of 9 units?

• 80 square units

• 72 square units

• 88 square units

• 64 square units

What geometric figure is formed by drawing a diagonal line through a rectangle?

• Pentagon

• Square

• Triangle

• Circle

If a rectangle has a perimeter of 28 units, what could be its length and width?

• Length: 8, Width: 6

• Length: 7, Width: 7

• Length: 10, Width: 4

• Length: 9, Width: 5