Question

foundations of geometry test
part i: measuring segments and angles

1. multiple choice

what is the length of segment ab if a is at (3, 2) and b is at (7, 6)?
use the formula: d = \sqrt{(x2 - x1)^2+(y2 - y1)^2}
a) 4
b) 5
c) 4\sqrt{32}
d) 4\sqrt{2}

Explanation:

Step1: Identify coordinates

Let $(x_1,y_1)=(3,2)$ and $(x_2,y_2)=(7,6)$.

Step2: Substitute into distance formula

$d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(7 - 3)^2+(6 - 2)^2}$.

Step3: Calculate values inside square - root

$(7 - 3)^2=4^2 = 16$ and $(6 - 2)^2=4^2 = 16$. Then $d=\sqrt{16 + 16}=\sqrt{32}$.

Step4: Simplify the square - root

$\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$.

Answer:

d) $4\sqrt{2}$