To find the distance between two points on a Cartesian plane, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is:
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
Given the two points (2,7) and (−2,0), let's plug in the coordinates into the distance formula. Here, \(x_1 = 2\), \(y_1 = 7\), \(x_2 = -2\), and \(y_2 = 0\).
\[d = \sqrt{(-2 - 2)^2 + (0 - 7)^2}\]
Compute the squares:
\[d = \sqrt{(-4)^2 + (-7)^2}\]
\[d = \sqrt{16 + 49}\]
Add the results:
\[d = \sqrt{65}\]
To get the distance to the nearest hundredth, let's calculate the square root:
\[d ≈ \sqrt{65} ≈ 8.06\]
So the distance between the points (2,7) and (−2, 0) is approximately 8.06 when rounded to the nearest hundredth. The correct response from the given options is:
8.06
8 point 0 6
Apply the Pythagorean Theorem to find the length between (2,7)
and (−2, 0)
. Round your answer to the nearest hundredth, if necessary.
Responses
11
11 - no response given
8.06
8 point 0 6 - correct
5.74
5 point 7 4 - no response given
65
1 answer