Triangles Online Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
13 of 1513 of 15 Items

Question
Apply the Pythagorean Theorem to find the length between (0, 6)
and (−3, −2)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

73
73

6.08
6.08

11
11

8.54

Answer 1

To find the distance between the points \((0, 6)\) and \((-3, -2)\), we can use the distance formula, which is derived from the Pythagorean Theorem. The formula is:

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

Here, \((x_1, y_1) = (0, 6)\) and \((x_2, y_2) = (-3, -2)\).

Now we substitute the coordinates into the formula:

1. Calculate \(x_2 - x_1\): \[ -3 - 0 = -3 \]

2. Calculate \(y_2 - y_1\): \[ -2 - 6 = -8 \]

3. Substitute these values into the distance formula: \[ d = \sqrt{(-3)^2 + (-8)^2} \] \[ d = \sqrt{9 + 64} \] \[ d = \sqrt{73} \]

Now, we can approximate \(\sqrt{73}\):

\[ \sqrt{73} \approx 8.54 \]

Thus, the answer, rounded to the nearest hundredth if necessary, is:

8.54