Question2-6: MathXL for School: Practice \& Problem Solving
Dec 31 - 11:59 pm
2.6.PS-14
Question Help
Freddy drew a plan for a rectangular piece of material that he will use for a blanket. Three of the vertices are , , and . What are the coordinates of the fourth vertex?
Studdy Solution
STEP 1
1. The shape is a rectangle.
2. Three vertices of the rectangle are given as , , and .
3. Opposite sides of a rectangle are equal and parallel.
STEP 2
1. Identify the pattern of the given vertices.
2. Determine the missing coordinate by using properties of a rectangle.
3. Verify the coordinates form a rectangle.
STEP 3
Identify the pattern of the given vertices:
- The first two vertices and have the same x-coordinate, indicating they are vertically aligned.
- The second and third vertices and have the same y-coordinate, indicating they are horizontally aligned.
STEP 4
Determine the missing coordinate:
- Since the rectangle's opposite sides are equal and parallel, the fourth vertex must share the x-coordinate with the third vertex and the y-coordinate with the first vertex.
- Therefore, the fourth vertex is .
STEP 5
Verify the coordinates form a rectangle:
- Check that opposite sides are equal:
- Vertical sides: to and to both have a length of .
- Horizontal sides: to and to both have a length of .
- Since opposite sides are equal, the shape is a rectangle.
The coordinates of the fourth vertex are:
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