Rectangle Properties and Coordinates

This video tutorial covers three main geometry problems. First, it explains how to find four possible endpoints for a line segment with a given length and one known endpoint. Next, it demonstrates how to determine the other two vertices of a rectangle when given two vertices and the perimeter. Finally, it tackles a more complex problem of finding the opposite vertex of a rectangle that contains the origin, given one vertex, the perimeter, and the area. The tutorial emphasizes understanding geometric properties and applying them to solve problems.

If one endpoint of a line segment is (-3, -6) and the segment is 7 units long, which of the following could be another endpoint?

• (4, -6)

• (0, 0)

• (7, -6)

• (-3, 0)

What is the coordinate of the endpoint if you move 7 units left from (-3, -6)?

• (-3, -6)

• (-3, 1)

• (-3, -13)

• (-10, -6)

Which point is reached by moving 7 units up from (-3, -6)?

• (-3, 1)

• (-10, -6)

• (-3, -13)

• (4, -6)

Given two vertices of a rectangle at (1, -6) and (-8, -6), what is the length of the side between these points?

• 9 units

• 10 units

• 8 units

• 7 units

If a rectangle has a perimeter of 26 units and one side is 9 units, what is the length of the other side?

• 7 units

• 6 units

• 4 units

• 5 units

What are the coordinates of the other two vertices of the rectangle with vertices (1, -6) and (-8, -6) and a perimeter of 26 units?

• (-8, -2) and (1, -2)

• (-8, -4) and (1, -4)

• (-8, -8) and (1, -8)

• (-8, -3) and (1, -3)

A rectangle has a perimeter of 28 units and an area of 48 square units. If one vertex is at (-5, -7), what are the possible dimensions of the rectangle?

• 6 by 8

• 5 by 9

• 7 by 7

• 4 by 12

Given a rectangle with one vertex at (-5, -7) and the origin inside, what is the opposite vertex if the rectangle is 6 by 8?

• (1, -7)

• (-5, 1)

• (0, 0)

• (1, 1)

If the origin is inside a rectangle with one vertex at (-5, -7), what must be true about the rectangle's dimensions?

• The rectangle must be a square

• The rectangle must be diagonal

• The longer side must be horizontal

• The longer side must be vertical

What is the opposite vertex of a rectangle with one vertex at (-5, -7) and dimensions 6 by 8?

• (1, 1)

• (0, 0)

• (1, -7)

• (-5, 1)