Question

use Pythagorean theorem to find the side length of c
a is -7,6
b is -2,-6

Answer 1

To use the Pythagorean theorem to find the length of side \( c \) in the context of a triangle formed by the points \( A(-7, 6) \) and \( B(-2, -6) \), we first need to calculate the length of side \( AB \) (the distance between points A and B).

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

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

Plugging in the coordinates for points A and B:

- \( (x_1, y_1) = (-7, 6) \)
- \( (x_2, y_2) = (-2, -6) \)

Now, substitute these values into the formula:

\[
d = \sqrt{((-2) - (-7))^2 + ((-6) - 6)^2}
\]

This simplifies to:

\[
d = \sqrt{(-2 + 7)^2 + (-6 - 6)^2}
\]
\[
d = \sqrt{(5)^2 + (-12)^2}
\]
\[
d = \sqrt{25 + 144}
\]
\[
d = \sqrt{169}
\]
\[
d = 13
\]

Thus, the distance (or length of side \( c \)) between points \( A \) and \( B \) is \( 13 \).

So, side length \( c \) is \( 13 \).