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 Ais (0,0),
Bis (a, 0), Cis (a, b), and Dis (0, b).
What formula can he use to determine the distance from
point A to point B?
A. (2-0)2 + (6-b)2 -
B. Via-0)2 + (0-0) - V-a
C. (2-0)2 + (0-0)2 =
D. V-0)? +(5-6)2 - 12 -
= a

Answer 1

`Distance = √((0 - a)^2 + (0 - 0)^2)`

`Distance = a`

Explanation:

Given

`A = (0,0)`

`B = (a,0)`

`C = (a,b)`

`D = (0,b)`

Required

Determine the distance between A and B

The distance between points is calculated as thus;

`Distance = √((x_1 - x_2)^2 + (y_1 - y_2)^2)`

Considering points A and B

`A(x_1,y_1) = (0,0)`

`B(x_2,y_2) = (a,0)`

Substitute values for
`x_1, x_2, y_1` and
`y_2` in the above formula

`Distance = √((0 - a)^2 + (0 - 0)^2)`

The above expression represents the distance between A and B;

However, it can be solved further as thus

`Distance = √(( -a)^2 + (0)^2)`

`Distance = √(a^2 + 0)`

`Distance = √(a^2)`

`Distance = a`

Hence, the distance between A and B is a