if the point (x,-1),(3,y),(-2,3)and (-3,-2) be the vertices of a parallelogram,then
Answers
Answer:
The given points are not vertices of a parallelogram.
Step-by-step explanation:
let, ABCD is a parallelogram.
x1,y1 =(x,-1) =AB
x2,y2=(3,y)=BC
x3,y3=(-2,3)=CD
x4,y4=(-3,-2)=AD
by the slope formula,
Slope of AB= y2-y1÷x2-x1
= y +1÷3-x
=1+y÷3-x
slope of BC =y3-y2÷x3-x2
=3-y÷-2-3
=3-y÷-5
slope of CD=y4-y3÷x4-x3
=-2-3÷-3+2
= -5÷-1
=5
slope of AD=y4-y1÷x4-x1
=-2+1÷-3-x
=-1÷-3-x
by the properties of parallelogram,
AB=CD AND BC=AD
1+y÷3-x=5 and 3-y÷-5=-1÷-3-x
AB is not equal to CD
BC is not equal to AD
then
point (x,-1) , (3,y), (-2,3) , (-3,-2) are not the vertices of a parallelogram.