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

Question

(-2, 3)
(-7, -9)
Responses
A 11
B 12
C 13
D 14
Question 2
Consider the two points (4, 6) and (−2, −2). Apply the Pythagorean theorem to find the distance between the points.
Responses
A 8
B 9
C 10
D 11

Answer 1

To find the distance between two points using the Pythagorean theorem, we can use the distance formula derived from it:

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

Question 1: Find the distance between the points \((-2, 3)\) and \((-7, -9)\).

1. Identify the coordinates:

   • \( (x_1, y_1) = (-2, 3) \)
   • \( (x_2, y_2) = (-7, -9) \)

2. Calculate the change in x and y:

   • \( x_2 - x_1 = -7 - (-2) = -7 + 2 = -5 \)
   • \( y_2 - y_1 = -9 - 3 = -12 \)

3. Plug these values into the distance formula: \[ d = \sqrt{(-5)^2 + (-12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \]

So, the answer is C 13.

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Question 2: Find the distance between the points \((4, 6)\) and \((-2, -2)\).

1. Identify the coordinates:

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

2. Calculate the change in x and y:

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

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

So, the answer is C 10.