Question

1. A quadrilateral has vertices A(0,0), B(8,0),C(7,5), and

Answer 1

The formula for the distance between two points is

$d(A,B) = \sqrt{(A_x-B_x)^2+(A_y-B_y)^2}$

Note that, if two points have one coordinate in common, this formula simplifies to

$d(A,B) = |A_x-B_x|,\quad d(A,B)=|A_y-B_y|$

(the first if they share the y coordinate, the second if they share the x coordinate).

So, these are the lengths of the sides:

$d(A,B)=|8-0|=8$

(because they share the y coordinate)

$d(B,C) = \sqrt{(8-7)^2+(0-5)^2}=\sqrt{1+25}=\sqrt{26}$

(standard formula)

$d(C,D)=|7-3|=4$

(because they share the y coordinate)

$d(A,D) = \sqrt{(0-3)^2+(0-5)^2}=\sqrt{9+25}=\sqrt{34}$