Show that a quadrilateral with the given vertices is a parallelogram. A(-2,0),B(-3,5),C(0,4),D(1,-1) Find the lengths of the sides of the quadrilateral.

Question

ST=

TU=

VU=

SV=



Answer 1

A(-2,0)B(-3,5),C(0,4),D(1,-1) the figure is a Parallelogram

The distance between two points P1 = (x1,y1) and P2 = (x2,y2) in the xy-plane is

√[(x2-x1)² + (y2-y1)²]

distance from A to B as A (-2,0) B (-3,5) = √[(-3- -2)²+(5-0)² ]

√(-1² + 5² ) = √ (1+25) = √26

so the length of the side AB = √26

B to C as B (-3,5) C (0,4) = √[(-3- 0)²+(5-4)² ]

√(-3² + 1² ) = √ (9+1) = √10 the length of the side BC = √10

C to D as C (0,4) D (1,-1)= √[(0- 1)²+(4- -1)² ]

√(-1² + 5² ) = √ (1+25) = √26 the length of the side CD = √26

D to A as A (-2,0) D (1,-1) = √[(-2- 1)²+(0- -1)² ]

√(-3² + 1² ) = √ (9+1) = √10 the length of the side DA = √10

Answer 2

Show that the slope of AB equals the slope of CD and t4he slope of BC equals the slope of DA.