The coordinates of the vertices of the triangle shown are A(1, 1), B(5, 1), and C(1, 5). Which measurement is closest to the length of CB in units?

Responses
A 4.7 units4.7 units
B 4.9 units4.9 units
C 5.7 units5.7 units
D 5.9 units

1 answer

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.