Find the distance between the points (-17, 10) and (-11, 8). Round your answer to the tenths place.
To find the distance between two points \(P_1 = (x_1, y_1)\) and \(P_2 = (x_2, y_2)\) in the Cartesian plane, we use the Euclidean distance formula:
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
Here, we are given the points \(P_1 = (-17, 10)\) and \(P_2 = (-11, 8)\).
Identifying the coordinates:
\(x_1 = -17, y_1 = 10\)
\(x_2 = -11, y_2 = 8\)
Substitute the coordinates of \(P_1\) and \(P_2\) into the distance formula:
\(\Delta x = x_2 - x_1 = -11 - (-17) = -11 + 17 = 6\)
\(\Delta y = y_2 - y_1 = 8 - 10 = -2\)
Now, square these differences:
\((\Delta x)^2 = 6^2 = 36\)
\((\Delta y)^2 = (-2)^2 = 4\)
Summing these squares gives:
\(36 + 4 = 40\)
Thus, the distance is \(d = \sqrt{40}\).
We need to evaluate \(\sqrt{40}\) and round to the nearest tenth:
\(\sqrt{40} \approx 6.324555\)
Rounding to the tenths place, we get \(6.3\).
Comparing this to the given options:
The calculated distance matches option b.
Imagine a map where your current location is at coordinate \((-17, 10)\) and your destination is at \((-11, 8)\). By calculating the distance between these two points using the Pythagorean theorem, you can determine how far you need to travel. With a calculated distance of \(\approx 6.3\) units, you can accurately estimate your travel time or fuel needs, ensuring you arrive at your destination efficiently.