A gridded coordinate plane is shown. 

The x and y axes are marked with bold black lines. 

Three points, labeled A, B, and C, are plotted on the grid, each marked with a yellow circle.

Point A is located at (3,0).

Point B is located at (0,3).

Point C is located at (0,5).

Apply the Pythagorean Theorem to find the distance between points A and C.
Responses
A units24 units
B units50 units
C units74 units
D units98 units

1 answer

To find the distance between points A and C using the Pythagorean Theorem, we first identify the coordinates of the points:

  • Point A is at (3, 0)
  • Point C is at (0, 5)

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:

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

Substituting in the coordinates of points A and C:

\[ d = \sqrt{(0 - 3)^2 + (5 - 0)^2} \]

Calculating the differences:

\[ d = \sqrt{(-3)^2 + (5)^2} \]

Calculating the squares:

\[ d = \sqrt{9 + 25} \]

Combining the values under the square root:

\[ d = \sqrt{34} \]

Evaluating \(\sqrt{34}\) gives approximately 5.83, which does not match any of the answer choices directly.

Since none of the provided responses directly correspond to the calculated distance, it seems there may be a misunderstanding regarding units or values provided. However, the distance between points A and C is indeed \( \sqrt{34} \) units.