To find the length of segment CB, we can use the distance formula. The coordinates of points C and B are:
- C(1, 5)
- B(5, 1)
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting in the coordinates of C and B:
- \(x_1 = 1\), \(y_1 = 5\)
- \(x_2 = 5\), \(y_2 = 1\)
Now calculate:
\[ d = \sqrt{(5 - 1)^2 + (1 - 5)^2} \] \[ = \sqrt{(4)^2 + (-4)^2} \] \[ = \sqrt{16 + 16} \] \[ = \sqrt{32} \] \[ = \sqrt{16 \times 2} \] \[ = 4\sqrt{2} \]
Calculating \(4\sqrt{2}\):
\[ \sqrt{2} \approx 1.414 \] So: \[ 4\sqrt{2} \approx 4 \times 1.414 \approx 5.656 \]
Thus, the length of CB is approximately 5.656 units.
The answer that is closest to this calculation is:
C: 5.7 units.