Find the distance between the coordinate points, a (two, 14) and B (10, three). Rounder answered to the nearest 10th.

Question

a^2+b^2=c^2

The distance between two points is_____ units.

Answer 1

To find the distance between the points \( A(2, 14) \) and \( B(10, 3) \), we can use the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Here, \( (x_1, y_1) = (2, 14) \) and \( (x_2, y_2) = (10, 3) \).

Now, substituting the values:

\[ d = \sqrt{(10 - 2)^2 + (3 - 14)^2} \] \[ d = \sqrt{(8)^2 + (-11)^2} \] \[ d = \sqrt{64 + 121} \] \[ d = \sqrt{185} \]

Next, we can find the approximate value of \( \sqrt{185} \):

\[ \sqrt{185} \approx 13.6 \]

Thus, the distance between the two points is approximately 13.6 units when rounded to the nearest tenth.

So, the final answer is:

The distance between two points is 13.6 units.