Question

Find the distance between the coordinate points A(2,14) and B(10, 3). Round your answer to the nearest tenth.

A^2 + B^2 = c^2

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:

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

where \( (x_1, y_1) \) are the coordinates of point A and \( (x_2, y_2) \) are the coordinates of point B.

Plugging in the coordinates:
- For point A, \( x_1 = 2 \) and \( y_1 = 14 \)
- For point B, \( x_2 = 10 \) and \( y_2 = 3 \)

Now we substitute these values into the distance formula:

\[
d = \sqrt{(10 - 2)^2 + (3 - 14)^2}
\]

Calculating the differences:

\[
d = \sqrt{(8)^2 + (-11)^2}
\]

Calculating the squares:

\[
d = \sqrt{64 + 121}
\]

Adding these:

\[
d = \sqrt{185}
\]

Now we calculate the square root:

\[
d \approx 13.6 \quad (\text{when rounded to the nearest tenth})
\]

Therefore, the distance between the points A(2, 14) and B(10, 3) is approximately \( \boxed{13.6} \) units.