Question

question 1 *

1. given ( g(-6,5) ) and ( h(2,-7) ), what is the length of ( overline{gh} )?

a. ( 4sqrt{13} )
b. ( 4sqrt{10} )
c. ( 2sqrt{5} )
d. ( 2sqrt{17} )
o a
o b
o c
o d

Explanation:

Step1: Identify the coordinates

Let \(G(-6,5)\) be \((x_1,y_1)\) and \(H(2,-7)\) be \((x_2,y_2)\).

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute the values: \(x_2 - x_1=2-(-6)=8\), \(y_2 - y_1=-7 - 5=-12\).
Then \(d=\sqrt{8^2+(-12)^2}=\sqrt{64 + 144}=\sqrt{208}\).

Step3: Simplify the square - root

\(\sqrt{208}=\sqrt{16\times13}=4\sqrt{13}\).

Answer:

A. \(4\sqrt{13}\)