Identifying Locations on a Coordinate Grid
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Gary labels places on the map using points. However, he has forgotten to put the names of each place. Gary wants to find out which point shows the bookstore. This is what he remembers about the bookstore's position:
- The x-coordinate and y-coordinate of the bookstore are different.
- The y-coordinate is greater than the x-coordinate.
- If he walks in one direction along the grid, starting from the bookstore, he will reach one of the other places labelled on the map.
The bookstore is at Point _____ ($ \_\_\_ , \_\_\_ $). Explain how you know.
This question includes visual content: A 2D coordinate grid with the x-axis ranging from 0 to 6 and the y-axis ranging from 0 to 6. The origin $(0,0)$ is in the top-left corner as depicted (axes are flipped/rotated compared to standard orientation in the image view). Five points are plotted and labeled with letters: point $O$ at $(2, 2)$, point $L$ at $(1, 4)$, point $M$ at $(5, 5)$, point $P$ at $(5, 3)$, and point $N$ at $(5, 6)$. A north arrow indicates directionality.
Animated Video Solution
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Step by Step Written Solution
In this problem, we need to find which point on the map represents the bookstore. Gary has given us three clues to figure it out.
Locating the Bookstore
First, let's list the coordinates for all the points we see on the grid. Remember that coordinates are written as x comma y.
| Point | Coordinates (x, y) |
|---|---|
| L | (4, 5) |
| M | (5, 2) |
| N | (5, 5) |
| O | (2, 2) |
| P | (1, 5) |
Now let's look at Gary's first clue: the x-coordinate and y-coordinate of the bookstore must be different.
Clue 1: x and y are different.
| Point | Coordinates |
|---|---|
| L | (4, 5) |
| M | (5, 2) |
| N | (5, 5) |
| O | (2, 2) |
| P | (1, 5) |
Point N has coordinates five five, and Point O has coordinates two two. Since their x and y values are the same, they cannot be the bookstore. Let's remove them.
The second clue is that the y-coordinate is greater than the x-coordinate.
Clue 2: y > x
For Point L, five is greater than four. For Point P, five is greater than one. But for Point M, two is NOT greater than five. So we can eliminate Point M.
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