Question
Raj plotted point L in the coordinate plane below.
On a coordinate plane, point L is 1.5 units to the left and 4 units up.
He says that the plotted point is (4, negative 1.5). What is Raj’s error?
The x-coordinate should be -4.
The y-coordinate should be 1.5.
The x- and y-coordinates are switched.
Both coordinates should be positive.
On a coordinate plane, point L is 1.5 units to the left and 4 units up.
He says that the plotted point is (4, negative 1.5). What is Raj’s error?
The x-coordinate should be -4.
The y-coordinate should be 1.5.
The x- and y-coordinates are switched.
Both coordinates should be positive.
Answers
GPT-4o mini
To analyze Raj’s error, let’s break down the position of point L:
- The description says that point L is 1.5 units **to the left** and 4 units **up**.
- Moving left on the x-axis implies a negative value, while moving up on the y-axis implies a positive value.
Starting from the origin (0, 0):
- Moving 1.5 units to the left means we move from 0 on the x-axis to -1.5, giving an x-coordinate of -1.5.
- Moving 4 units up means we move from 0 on the y-axis to 4, giving a y-coordinate of 4.
Thus, the correct coordinates for point L should be (-1.5, 4).
Now let’s analyze Raj’s coordinates, which he stated as (4, -1.5):
- The x-coordinate is positive when it should be negative.
- The y-coordinate is negative when it should be positive.
From this analysis, we find that:
1. The x-coordinate should be -1.5 (should be negative).
2. The y-coordinate should be 4 (should be positive).
Looking at the options given:
1. The x-coordinate should be -4. (Incorrect)
2. The y-coordinate should be 1.5. (Incorrect)
3. The x- and y-coordinates are switched. (Incorrect)
4. Both coordinates should be positive. (Incorrect)
The closest match regarding Raj's error (since no option directly states that x should be -1.5 and y should be 4) is that his understanding of the quadrant or the signs in coordinates was incorrect.
None of the available options on Raj's error specifically capture the explanation above regarding the coordinates being calculated incorrectly based on movement directions.
Ultimately, Raj's error is primarily regarding the signs of the x- and y-coordinates.
- The description says that point L is 1.5 units **to the left** and 4 units **up**.
- Moving left on the x-axis implies a negative value, while moving up on the y-axis implies a positive value.
Starting from the origin (0, 0):
- Moving 1.5 units to the left means we move from 0 on the x-axis to -1.5, giving an x-coordinate of -1.5.
- Moving 4 units up means we move from 0 on the y-axis to 4, giving a y-coordinate of 4.
Thus, the correct coordinates for point L should be (-1.5, 4).
Now let’s analyze Raj’s coordinates, which he stated as (4, -1.5):
- The x-coordinate is positive when it should be negative.
- The y-coordinate is negative when it should be positive.
From this analysis, we find that:
1. The x-coordinate should be -1.5 (should be negative).
2. The y-coordinate should be 4 (should be positive).
Looking at the options given:
1. The x-coordinate should be -4. (Incorrect)
2. The y-coordinate should be 1.5. (Incorrect)
3. The x- and y-coordinates are switched. (Incorrect)
4. Both coordinates should be positive. (Incorrect)
The closest match regarding Raj's error (since no option directly states that x should be -1.5 and y should be 4) is that his understanding of the quadrant or the signs in coordinates was incorrect.
None of the available options on Raj's error specifically capture the explanation above regarding the coordinates being calculated incorrectly based on movement directions.
Ultimately, Raj's error is primarily regarding the signs of the x- and y-coordinates.