Question

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

Answer 1

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.**