Help Mr. Hibbard!
Mr. Hibbard was finding the distance between the points (6, 2) and (1, −4)
, as seen in his work below. Is the distance correct?
(1 point)
Responses
Yes, the work was correctly done.
Yes, the work was correctly done.
No, the numbers in the first line are incorrect. It should be (6−1)2 − (2+4)2−−−−−−−−−−−−−−−−√
No, the numbers in the first line are incorrect. It should be (6−1)2 − (2+4)2−−−−−−−−−−−−−−−−√
No, the numbers in the first line are incorrect. It should be (6−1)2 + (2+4)2−−−−−−−−−−−−−−−−√
.
No, the numbers in the first line are incorrect. It should be (6−1)2 + (2+4)2−−−−−−−−−−−−−−−−√
.
Yes, the work was correctly done, but the find answer should not be a decimal.
Yes, the work was correctly done, but the find answer should not be a decimal.
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The correct response is: No, the numbers in the first line are incorrect. It should be (6-1)^2 + (2-(-4))^2.
No, the numbers in the first line are incorrect. It should be (6−1)2 + (2+4)2−−−−−−−−−−−−−−−−√.
To find the distance between two points in the Cartesian coordinate system, Mr. Hibbard used the distance formula, which is given by:
distance = √((x2 - x1)² + (y2 - y1)²)
In this formula, (x1, y1) represents the coordinates of the first point, and (x2, y2) represents the coordinates of the second point.
Let's use Mr. Hibbard's work to check if the distance was calculated correctly.
He started by substituting the given coordinates into the distance formula:
distance = √((6 - 1)² + (2 - (-4))²)
Simplifying this expression gives:
distance = √((5)² + (2 + 4)²)
Now we need to calculate the squares and the sum:
distance = √(25 + 36)
Finally, we find the square root of the sum:
distance = √61
So, according to Mr. Hibbard's work, the distance between the points (6, 2) and (1, -4) is √61, which is an irrational number and cannot be further simplified.
Therefore, the correct answer is: No, the numbers in the first line are incorrect. It should be (6 - 1)² + (2 - (-4))²√.