Apply the Pythagorean theorem to find the distance between the two points shown on the graph.

Question

Responses
A 1111
B 1212
C 1313
D 1414
Question 2
Consider the two points (4, 6) and (−2, −2). Apply the Pythagorean theorem to find the distance between the points.
Responses
A 88
B 99
C 1010
D 11

Answer 1

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) using the Pythagorean theorem, you can use the distance formula:

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

For Question 2, the points are \((4, 6)\) and \((-2, -2)\).

1. First, identify the coordinates:

   • \(x_1 = 4\), \(y_1 = 6\)
   • \(x_2 = -2\), \(y_2 = -2\)

2. Calculate the differences:

   • \(x_2 - x_1 = -2 - 4 = -6\)
   • \(y_2 - y_1 = -2 - 6 = -8\)

3. Apply the distance formula: \[ d = \sqrt{(-6)^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \]

Therefore, the answer for Question 2 is C: 10.

For Question 1, to find the distance between the two unspecified points on the graph, you'll need their coordinates to apply the same method, so please provide the coordinates of these points.