Question

use the right triangle abc to find the length of the line segment between point a and point b. you just found the length of the hypotenuse, c. thats the length of the line segment between point a and point b. label that on the coordinate plane. the coordinate plane has points b(-1,5), c(7,5), a(7,-3). the formula a² + b² = c² is used, with 8² + 8² = c², so c = √128.

Explanation:

Step1: Simplify the square root

We know that \( c = \sqrt{128} \). We can factor 128 into \( 64\times2 \), since \( 64\times2 = 128 \).

Step2: Use the square root property

Using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a = 64 \) and \( b = 2 \)), we get \( \sqrt{128}=\sqrt{64\times2}=\sqrt{64}\times\sqrt{2} \).
Since \( \sqrt{64} = 8 \), then \( \sqrt{128}=8\sqrt{2} \approx 11.31 \) (if we want a decimal approximation). But the simplified radical form is \( 8\sqrt{2} \).

Answer:

\( 8\sqrt{2} \) (or approximately \( 11.31 \))