Find the distance between the coordinate points A(2, 14) and B(10, 3). Round your answer to the nearest tenth. A graph representation of the points (2, 14) and (10, 3) for you to find the distance between.

Question

a2+b2=c2

[Click Here if you would like to create a different visual] (although it is not needed to solve at all!)

(1 point)
The distance between the 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, which is given by:

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

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

Now, let's apply the formula:

1. Subtract the x-coordinates: \[ x_2 - x_1 = 10 - 2 = 8 \]

2. Subtract the y-coordinates: \[ y_2 - y_1 = 3 - 14 = -11 \]

3. Now, substitute these values into the distance formula: \[ d = \sqrt{(8)^2 + (-11)^2} \] \[ d = \sqrt{64 + 121} \] \[ d = \sqrt{185} \]

4. Calculate the square root of 185: \[ d \approx 13.6 \quad (\text{rounded to the nearest tenth}) \]

So, the distance between the two points is approximately 13.6 units.