Difference between revisions of "2019 AMC 10B Problems/Problem 5"
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+ | Triangle <math>ABC</math> lies in the first quadrant. Points <math>A</math>, <math>B</math>, and <math>C</math> are reflected across the line <math>y=x</math> to points <math>A'</math>, <math>B'</math>, and <math>C'</math>, respectively. Assume that none of the vertices of the triangle lie on the line <math>y=x</math>. Which of the following statements is not always true? | ||
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+ | <math>\textbf{(A) } </math> Triangle <math>A'B'C'</math> lies in the first quadrant. | ||
+ | <math>\textbf{(B) } </math> Triangles <math>ABC</math> and <math>A'B'C'</math> have the same area. | ||
+ | <math>\textbf{(C) } </math> The slope of line <math>AA'</math> is <math>-1</math>. | ||
+ | <math>\textbf{(D) } </math> The slopes of lines <math>AA'</math> and <math>CC'</math> are the same. | ||
+ | <math>\textbf{(E) } </math> Lines <math>AB</math> and <math>A'B'</math> are perpendicular to each other. | ||
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+ | ==Solution== | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{AMC10 box|year=2019|ab=B|num-b=4|num-a=6}} | ||
+ | {{MAA Notice}} |
Revision as of 15:32, 14 February 2019
Problem
Triangle lies in the first quadrant. Points , , and are reflected across the line to points , , and , respectively. Assume that none of the vertices of the triangle lie on the line . Which of the following statements is not always true?
Triangle lies in the first quadrant. Triangles and have the same area. The slope of line is . The slopes of lines and are the same. Lines and are perpendicular to each other.
Solution
See Also
2019 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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