Question

the following quadrilateral has vertices the points (7,3), (3,0), (0,-4) and (4,-1). using slopes prove that the mid points of the sides of quadrilateral form a parallelogram.​

Answer 1

Answer:

Step-by-step explanation:

The mid point of parallelogram is

A=  (-4,2) =

B = (5,1) =

C =(6,5) =

D = (-7,6) =

AB= -4+5/2, -2-1/2

P = 1/2,-3/2

BC = 5+6/2, -1+5/2

Q = 11/2, 4/2

CD = 6-7/2, 5+6/2

R = -1/2, 11/2

DA = -7-4/2, -2+6/2

S= 11/2,4/2

Hence if the slope of the opposite sides are equal then gives the vertices of parallelogram

Slop of PQ =  RS

Slope of PS = QR

Slop of PQ is 4/2(-3/2)/11/2-1/2 += 7/10

Slope of RS is

4/2-11/2/-11/2-(-1/2) = 7/10

Slop of PS 4/2/-(-3/2)/-11/2-1/2 = -7/12

Slope of QR is 11/2-4/2/-1/2-11/2 = -7/12

Therefore slope of opposite sides are equal

Midpoint of quadrilateral of forms a parallelogram.