Question

if A(-4,2),B(2,0),C(8,6) and D(a,b) are the vertices of a parallelogram ABCD then a and b are​

Answer 1

Answer:

Midpoint of AB,BC, CD and DA are `P(-1,4), Q(5,(11)/(2)),R((17)/(2),-1) and S((5)/(2),(5)/(2))`

Now, show that (slope of PQ=slope of RS=`(1)/(4))` and (slope of QR=slope of PS=`((-13)/(7))`.

Step-by-step explanation:

hope that it is correct

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Answer 2

Given:

A(-4,2)

B(2,0)

C(8,6)

D(a ,b)

A, B, C and D are the vertices of a parallelogram ABCD

Find a and b=?

We know that In a parallelogram the diagonals bisect each other

so Midpoint of AC = midpoint of BD

$(\frac{-4+8}{2} ,\frac{2+6}{2} ) = (\frac{2+a}{2} ,\frac{0+b}{2} )$

$(\frac{4}{2}, \frac{8}{2} )=(\frac{a+2}{2} ,\frac{b}{2} )$

$(2,4)=(\frac{a+2}{2} ,\frac{b}{2} )$

$\frac{a+2}{2}=2 \ and \ \frac{b}{2} =4$

So  for find the value of "a"  

a+2 = 2 × 2

a + 2=4

a = 4 - 2

a = 2

for find the value of "b"

b = 4 × 2

b = 8

Hence the value of a is 2 and the value of b is 8