Math Problem Statement
The locations of the vertices of quadrilateral LMNP are L(0, 0), M(2, 4), N(8, 6), and P(6, 2). Quadrilateral STUV is congruent to LMNP. What are the lengths of the diagonals of quadrilateral STUV?
Solution
To determine the lengths of the diagonals of quadrilateral , we first need to compute the lengths of the diagonals of quadrilateral since the two quadrilaterals are congruent. Congruent quadrilaterals have equal corresponding side lengths and diagonal lengths.
Step 1: Identify the diagonals of
The diagonals of quadrilateral connect the following pairs of vertices:
- Diagonal 1: to
- Diagonal 2: to
Step 2: Compute the lengths of the diagonals
To calculate the lengths of the diagonals, we use the distance formula: where and are the coordinates of the two points.
Diagonal 1: to
Diagonal 2: to
Step 3: Conclusion
Since quadrilateral is congruent to quadrilateral , the lengths of the diagonals of are the same as those of :
- Length of Diagonal 1:
- Length of Diagonal 2:
Do you want further details or have any questions?
Here are five related questions to extend this topic:
- How would you compute the perimeter of quadrilateral ?
- What is the area of quadrilateral ?
- How do you prove two quadrilaterals are congruent?
- How can you find the coordinates of quadrilateral if given a transformation?
- How do you find the angles within a quadrilateral based on its vertex coordinates?
Tip: When using the distance formula, double-check the signs of the coordinates to avoid calculation errors.
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Math Problem Analysis
Mathematical Concepts
Geometry
Congruence
Distance Formula
Quadrilaterals
Formulas
Distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
Theorems
Congruent figures have equal corresponding side lengths and diagonals
Suitable Grade Level
Grades 8-10
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