2023 AMC 8 Problem 7

Below is the video solution and professionally curated solution for Problem 7 of the 2023 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2023 AMC 8 solutions, or check the answer key.

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Concepts:coordinate geometry linear equation

Difficulty rating: 1070

A rectangle, with sides parallel to the $x$ -axis and $y$ -axis, has opposite vertices located at $(15, 3)$ and $(16, 5).$ A line is 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?

$0$

$1$

$2$

$3$

$4$

Video solution:

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Written solution:

We can graph the two lines.

From this, we see that only the top left corner of the rectangle intersects either line.

Thus, B is the correct answer.

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