Difference between revisions of "2023 AMC 8 Problems/Problem 7"

(Solution)
(Solution)
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If we extend the lines, we have
 
If we extend the lines, we have
  
[[Image:Screenshot 2023-01-25 8.26.48 AM.png|thumb|center|200px]]
+
[[Image:Screenshot 2023-01-25 8.26.48 AM.png|thumb|center|400px]]
  
 
Hence, we see that the answer is <math>\boxed{\textbf{(B)}\ 1}</math>
 
Hence, we see that the answer is <math>\boxed{\textbf{(B)}\ 1}</math>

Revision as of 08:30, 25 January 2023

Problem

A rectangle, with sides parallel to the $x$-axis and $y$-axis, has opposite vertices located at $(15, 3)$ and $(16, 5)$. A line drawn through points $A(0, 0)$ and $B(3, 1)$. Another line is drawn through points $C(0, 10)$ and $D(2, 9)$. How many points on the rectangle lie on at least one of the two lines?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 4$

Solution

If we extend the lines, we have

Screenshot 2023-01-25 8.26.48 AM.png

Hence, we see that the answer is $\boxed{\textbf{(B)}\ 1}$

~MrThinker

See Also

2023 AMC 8 (ProblemsAnswer KeyResources)
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 AJHSME/AMC 8 Problems and Solutions

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