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 Responses There are no mistakes. The distance of -14.9 is correct. There are no mistakes. The distance of -14.9 is correct. Step 1 should have (10−5)2 as the second parenthesis. Step 1 should have open paren 10 minus 5 close paren squared as the second parenthesis. 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.
There is an error, and the first mistake was made in Step 1.
The correct distance formula for points (x1, y1) and (x2, y2) is:
d = √((x2 - x1)² + (y2 - y1)²)
Applying the distance formula to points (2, -5) and (4, 10) should look like this:
Step 1: d = √((4 - 2)² + (10 - (-5))²)
Step 1 Corrected: d = √((2)² + (15)²)
Step 2: d = √(4 + 225)
Step 3: d = √229
Step 4: d is approximately equal to 15.13
The original Step 1 incorrectly subtracted the y-values and placed a minus sign between the squared differences of the x-values and y-values. It should be an addition sign between them because you are summing the squares of the differences between the respective x and y coordinate values.
Therefore, the correct response is:
The distance formula has addition in between the parentheses, so step 1 should be d = √((4 − 2)² + (10 − (-5))²).