Bot GPT 4-o mini To determine the length of the segment AC, we can use the distance formula. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, point A is at \((-3, 3)\) and point C is at \((1, 6)\).
Let’s plug in these coordinates into the formula:
- \(x_1 = -3\), \(y_1 = 3\)
- \(x_2 = 1\), \(y_2 = 6\)
Now substituting these values into the distance formula:
\[ d = \sqrt{(1 - (-3))^2 + (6 - 3)^2} \] \[ = \sqrt{(1 + 3)^2 + (3)^2} \] \[ = \sqrt{(4)^2 + (3)^2} \] \[ = \sqrt{16 + 9} \] \[ = \sqrt{25} \] \[ = 5 \]
Therefore, the length of AC is 5.
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