Question
Error analysis:
To find the distance between points (2, -5) and (4, 10), the following steps were used.
Is the distance correct? If the distance is not correct, where was the FIRST mistake made?
Step 1: d=(4−2)2−(10+5)2−−−−−−−−−−−−−−−−√
Step 2: d=(2)2−(15)2−−−−−−−−−−√
Step 3: d=4−225−−−−−−√
Step 4: d=−221−−−−√
Step 5: d=−14.9
(1 point)
Responses
There are no mistakes. The distance of -14.9 is correct.
There are no mistakes. The distance of -14.9 is correct.
The distance formula has addition in between the parenthesis, so step 1 should be d=(4−2)2+(10+5)2−−−−−−−−−−−−−−−−√
.
The distance formula has addition in between the parenthesis, so step 1 should be d is equal to square root of open paren 4 minus 2 close paren squared plus open paren 10 plus 5 close paren squared end root.
In step 2, (15)2
means multiply 15 times 2 to get 30 instead of 225 for step 3.
In step 2, 15 squared means multiply 15 times 2 to get 30 instead of 225 for step 3.
Step 1 should have (10−5)2
as the second parenthesis.
To find the distance between points (2, -5) and (4, 10), the following steps were used.
Is the distance correct? If the distance is not correct, where was the FIRST mistake made?
Step 1: d=(4−2)2−(10+5)2−−−−−−−−−−−−−−−−√
Step 2: d=(2)2−(15)2−−−−−−−−−−√
Step 3: d=4−225−−−−−−√
Step 4: d=−221−−−−√
Step 5: d=−14.9
(1 point)
Responses
There are no mistakes. The distance of -14.9 is correct.
There are no mistakes. The distance of -14.9 is correct.
The distance formula has addition in between the parenthesis, so step 1 should be d=(4−2)2+(10+5)2−−−−−−−−−−−−−−−−√
.
The distance formula has addition in between the parenthesis, so step 1 should be d is equal to square root of open paren 4 minus 2 close paren squared plus open paren 10 plus 5 close paren squared end root.
In step 2, (15)2
means multiply 15 times 2 to get 30 instead of 225 for step 3.
In step 2, 15 squared means multiply 15 times 2 to get 30 instead of 225 for step 3.
Step 1 should have (10−5)2
as the second parenthesis.
Answers
GPT-4o mini
The correct response is:
**The distance formula has addition in between the parentheses, so step 1 should be \( d = \sqrt{(4−2)^2 + (10−(-5))^2} \).**
Here, the distance formula for finding the distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case, the correct calculations should have been as follows:
1. Substitute the points \((2, -5)\) and \((4, 10)\) into the distance formula:
\[
d = \sqrt{(4 - 2)^2 + (10 - (-5))^2}
\]
2. Calculate the differences:
\[
d = \sqrt{(2)^2 + (10 + 5)^2}
\]
3. This simplifies to:
\[
d = \sqrt{(2)^2 + (15)^2}
\]
4. Resulting in:
\[
d = \sqrt{4 + 225} = \sqrt{229}
\]
The initial mistake was in Step 1, where the addition should have been used for the \(y\) coordinates instead of incorrectly using subtraction and incorrectly forming the expression.
**The distance formula has addition in between the parentheses, so step 1 should be \( d = \sqrt{(4−2)^2 + (10−(-5))^2} \).**
Here, the distance formula for finding the distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case, the correct calculations should have been as follows:
1. Substitute the points \((2, -5)\) and \((4, 10)\) into the distance formula:
\[
d = \sqrt{(4 - 2)^2 + (10 - (-5))^2}
\]
2. Calculate the differences:
\[
d = \sqrt{(2)^2 + (10 + 5)^2}
\]
3. This simplifies to:
\[
d = \sqrt{(2)^2 + (15)^2}
\]
4. Resulting in:
\[
d = \sqrt{4 + 225} = \sqrt{229}
\]
The initial mistake was in Step 1, where the addition should have been used for the \(y\) coordinates instead of incorrectly using subtraction and incorrectly forming the expression.