Question

the coordinate grid shows $overline{xy}$. which measurement is closest to the length of $overline{xy}$ in units? a 7.8 units b 11.7 units c 16.0 units d 13.0 units

Explanation:

Step1: Identify coordinates

Let \(Y(-5,0)\) and \(X(5,6)\).

Step2: Apply distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1=-5,y_1 = 0,x_2=5,y_2 = 6\). So \(d=\sqrt{(5-(-5))^2+(6 - 0)^2}=\sqrt{(5 + 5)^2+6^2}=\sqrt{10^2+6^2}=\sqrt{100 + 36}=\sqrt{136}\).

Step3: Calculate the square - root

\(\sqrt{136}\approx11.66\).

Answer:

B. 11.7 units