Question

given: the coordinates of rectangle defg are d(0, b), e(a, b), f(a, 0), and g(0, 0). prove: the diagonals of a rectangle are congruent. as part of the proof, find the length of (overline{ge}). (sqrt{a + b}) (sqrt{a^{2}+b^{2}}) (sqrt{a - b}) (sqrt{a^{2}-b^{2}})

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Identify coordinates of G and E

Given $G(0,0)$ and $E(a,b)$. Here $x_1 = 0,y_1 = 0,x_2=a,y_2 = b$.

Step3: Substitute into distance formula

$d=\sqrt{(a - 0)^2+(b - 0)^2}=\sqrt{a^{2}+b^{2}}$.

Answer:

$\sqrt{a^{2}+b^{2}}$