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
`√(13)` cm, BC
`√(13)` cm, CD 2
`√(13)` cm and DA
`√(13)` cm

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 =
`√(52)` cm = 2
`√(13)` cm

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

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

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