Question

In the coordinate plane, quadrilateral ABCD has vertices with coordinates A(1,−1), B(−5,3), C(−3,6), and D(3,2). ​ ​Part A: Compute the lengths of the sides of quadrilateral ABCD.

Answer 1

The lengths are AB 2$\sqrt{13}$ cm, BC $\sqrt{13}$ cm, CD 2$\sqrt{13}$ cm and DA $\sqrt{13}$ cm

Step-by-step explanation:

Given,

The vertices of quadrilateral are A(1,-1), B(-5,3), C(-3,6) and D(3,2)

To find the lengths of the sides of ABCD

Formula

The length of two points (x1,y1) and (x2,y2) is $\sqrt{(x1-x2)^{2} +(y1-y2)^{2} }$

So,

AB ⇒$\sqrt{(1+5)^{2} +(-1-3)^{2} }$ cm = $\sqrt{52}$ cm = 2$\sqrt{13}$ cm

BC ⇒$\sqrt{(-5+3)^{2}+(3-6)^{2} }$ cm = $\sqrt{13}$ cm

CD ⇒$\sqrt{(-3-3)^{2} +(6-2)^{2} }$ cm = $\sqrt{52}$ cm = 2$\sqrt{13}$ cm

DA ⇒$\sqrt{(3-1)^{2}+(2+1)^{2} }$ cm = $\sqrt{13}$ cm