Find the distance between point

Question

A
(
−
5
,

7
)
A(−5, 7) and
B
(
7
,

11
)
B(7, 11). Round your answer to the nearest tenth. Click Here for Help Video. Click Here if you would like to create a visual.

Answer 1

To find the distance between two points \( A(-5, 7) \) and \( B(7, 11) \), you can use the distance formula:

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

where

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

Substituting the coordinates of points A and B into the formula:

1. Identify the coordinates:

   • \( x_1 = -5 \), \( y_1 = 7 \)
   • \( x_2 = 7 \), \( y_2 = 11 \)

2. Plug in the values: \[ d = \sqrt{(7 - (-5))^2 + (11 - 7)^2} \]

3. Simplify: \[ = \sqrt{(7 + 5)^2 + (11 - 7)^2} \] \[ = \sqrt{(12)^2 + (4)^2} \] \[ = \sqrt{144 + 16} \] \[ = \sqrt{160} \]

4. Now calculate \( \sqrt{160} \): \[ \sqrt{160} \approx 12.649 \]

5. Round to the nearest tenth: \[ \approx 12.6 \]

So, the distance between points \( A(-5, 7) \) and \( B(7, 11) \) is approximately 12.6.