Problem Analysis:
The task involves identifying the coordinates of various Christmas-themed items on a grid and using clues to determine the location of Santa's secret grotto. Let's break it down step by step.
---
Step 1: Write Down the Coordinates of Each Item on the Grid
We need to identify the coordinates of each item on the grid. The grid uses a standard Cartesian coordinate system, where the horizontal axis (x-axis) represents the column number, and the vertical axis (y-axis) represents the row number. The origin (0, 0) is at the bottom-left corner.
#### Items and Their Coordinates:
1.
Christmas Tree:
- Located at column 9, row 4.
- Coordinates:
(9, 4)
2.
Snowman:
- Located at column 7, row 1.
- Coordinates:
(7, 1)
3.
Snowflake:
- Located at column 1, row 9.
- Coordinates:
(1, 9)
4.
Candy Cane:
- Located at column 3, row 2.
- Coordinates:
(3, 2)
5.
Holly Leaf:
- Located at column 5, row 8.
- Coordinates:
(5, 8)
6.
Star:
- Located at column 7, row 10.
- Coordinates:
(7, 10)
7.
Reindeer:
- Located at column 2, row 6.
- Coordinates:
(2, 6)
8.
Bell:
- Located at column 8, row 7.
- Coordinates:
(8, 7)
9.
Sheep:
- Located at column 0, row 1.
- Coordinates:
(0, 1)
---
Step 2: Use the Clues to Find the Location of Santa’s Secret Grotto
The clues provided are:
1. It is north of the tree and south of the star.
2. It is east of the reindeer and west of the holly leaf.
3. It is in a direct line north-east of the sheep.
#### Clue Analysis:
1.
North of the tree and south of the star:
- The tree is at
(9, 4).
- The star is at
(7, 10).
- The grotto must be between rows 4 and 10, but closer to row 4 than row 10.
2.
East of the reindeer and west of the holly leaf:
- The reindeer is at
(2, 6).
- The holly leaf is at
(5, 8).
- The grotto must be between columns 2 and 5, but closer to column 5 than column 2.
3.
In a direct line north-east of the sheep:
- The sheep is at
(0, 1).
- A north-east direction means moving diagonally up and to the right.
- Starting from
(0, 1), possible coordinates in a north-east direction are:
(1, 2),
(2, 3),
(3, 4),
(4, 5),
(5, 6), etc.
#### Combining the Clues:
- From Clue 1: The grotto is between rows 4 and 10.
- From Clue 2: The grotto is between columns 2 and 5.
- From Clue 3: The grotto is on the diagonal path starting from
(0, 1).
The only coordinate that satisfies all three conditions is
(4, 5):
- It is north of the tree (
9, 4) and south of the star (
7, 10).
- It is east of the reindeer (
2, 6) and west of the holly leaf (
5, 8).
- It lies on the north-east diagonal path from the sheep (
0, 1).
---
Final Answer:
1. Coordinates of the items:
- Christmas Tree:
(9, 4)
- Snowman:
(7, 1)
- Snowflake:
(1, 9)
- Candy Cane:
(3, 2)
- Holly Leaf:
(5, 8)
- Star:
(7, 10)
- Reindeer:
(2, 6)
- Bell:
(8, 7)
- Sheep:
(0, 1)
2. Coordinates of Santa’s secret grotto:
(4, 5)
$$
\boxed{(4, 5)}
$$
Parent Tip: Review the logic above to help your child master the concept of 4th grade math activities.
