Math Problem Statement
Solution
The image shows a parallelogram ABCD on a coordinate plane with the points labeled as follows:
- Point A (-11, 23)
- Point B (-13, 29)
- Point C (5, 22)
You are asked to find the coordinates of point D.
Solution:
In a parallelogram, opposite sides are parallel and equal in length. Thus, the vector from A to B is equal to the vector from D to C. We can find the coordinates of point D by using this property.
The vector from A to B is:
Since , the vector from D to C must also be (-2, 6). Therefore, to find D, we can apply the vector to point C:
Thus, the coordinates of point D are (7, 16).
Let me know if you need further clarification or details! Also, here are a few related questions:
- What is the general formula for finding the coordinates of a point in a parallelogram?
- How do you find the area of a parallelogram given its vertex coordinates?
- What is the distance between two points in a coordinate plane?
- How do you determine if a quadrilateral is a parallelogram from its vertex coordinates?
- How can you prove that opposite sides of a parallelogram are parallel using vectors?
Tip: When dealing with parallelograms, always remember that opposite sides are not only parallel but also equal in length. This can help simplify many problems like this one.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Vectors
Properties of Parallelograms
Formulas
Vector addition/subtraction formula: (x2 - x1, y2 - y1)
Theorems
Opposite sides of a parallelogram are equal and parallel
Suitable Grade Level
Grade 9-10
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