Question

miguel wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. he places parallelogram abcd in the coordinate plane so that a is (0, 0), b is (a, 0), c is (a, b), and d is (0, b).
what formula can he use to determine the distance from point a to point b?
a. $(a-0)^2+(b-b)^2=a^2$
b. $sqrt{(a-0)^2+(b-b)^2}=sqrt{a^2}=a$
c. $sqrt{(a-0)^2+(0-0)^2}=sqrt{a^2}=a$
d. $(a-0)^2+(0-0)^2=a^2$

Explanation:

Step1: Recall distance formula

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

Step2: Substitute A(0,0) and B(a,0)

Substitute $x_1=0,y_1=0,x_2=a,y_2=0$ into the formula:
$\sqrt{(a-0)^2+(0-0)^2} = \sqrt{a^2} = a$

Answer:

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