2000 AMC 10 Problems/Problem 5
Problem
Points and are the midpoints of sides and of . As moves along a line that is parallel to side , how many of the four quantities listed below change?
(a) the length of the segment
(b) the perimeter of
(c) the area of
(d) the area of trapezoid
Solution
(a) Triangles and are similar, and since , .
(b) We see the perimeter changes. For example, imagine if P was extremely far to the left.
(c) The area clearly doesn't change, as both the base and its corresponding height remain the same.
(d) The bases and do not change, and neither does the height, so the area of the trapezoid remains the same.
Only quantity changes, so the correct answer is .
See Also
2000 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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