Lulu marks the points  (9,2)  and  (3,6)  on the coordinate plane. What is the distance between these two points, rounded to the nearest tenth of a unit?(1 point)Responses10.0 units10.0 units7.8 units7.8 units7.2 units7.2 units6.0 units

1 answer

To find the distance between the points \( (9, 2) \) and \( (3, 6) \), we can use the distance formula:

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

Here, we set:

  • \( (x_1, y_1) = (9, 2) \)
  • \( (x_2, y_2) = (3, 6) \)

Now, substituting in the values:

\[ d = \sqrt{(3 - 9)^2 + (6 - 2)^2} \] \[ d = \sqrt{(-6)^2 + (4)^2} \] \[ d = \sqrt{36 + 16} \] \[ d = \sqrt{52} \]

Now calculate \( \sqrt{52} \):

\[ \sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13} \]

Next, we can approximate \( \sqrt{13} \). The approximate value of \( \sqrt{13} \) is about \( 3.605551275 \), so:

\[ 2\sqrt{13} \approx 2 \times 3.605551275 \approx 7.21110255 \]

Rounding to the nearest tenth, we find:

\[ d \approx 7.2 \]

Thus, the distance between the points \( (9, 2) \) and \( (3, 6) \) is approximately 7.2 units.