Question

Find the length of the diagonal BD in the quadrilateral ABCD shown in the coordinate plane ?

Answer 1

bearing in mind B is at (4,3) and D is at (-2,-4).

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad D(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ BD=\sqrt{(-2-4)^2+(-4-3)^2}\implies BD=\sqrt{(-6)^2+(-7)^2} \\\\\\ BD=\sqrt{36+49}\implies BD=\sqrt{85}$

Answer 2

Answer: $\sqrt{37}\text{ units}$

Step-by-step explanation:

Distance formula : The distance between two points P(a,b) and Q(c,d) is given by :-

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

From the graph , the coordinated of point B = (4,3)

and the coordinates of D = (-2,4)

Then , $BD=\sqrt{(4-3)^2+(-2-4)^2}$

$BD=\sqrt{(1)^2+(-6)^2}=\sqrt{1+36}=\sqrt{37}\text{ units}$

Hence, the length of the diagonal BD in the quadrilateral ABCD = $\sqrt{37}\text{ units}$