Question

if p(a-1,2)and Q(2,b-2) are coincident points then the value of a and b respectively are​

Answer 1

Answer:

Consider the given points A(1,−2),B(2,3),C(0,2) and D(−4,−3)

Since ABCD form a parallelogram, the midpoint of the diagonal AC should coincide with the midpoint of BD.

Mid point of AC= Mid point of BD

[21+a​,2−2+2​]=[22−4​,23−3​]

[2a+1​,0]=[2−2​,0]

Since the mid points coincide, we have

21+a​=a

⇒a+1=−2

⇒a=−2−1

⇒a=−3

Now, area of ΔABC

=21​∣x1​(y2​−y3​)+x2​(y3​−y1​)+x3​(y1​−y2​)∣

=21​∣1(3−2)+2(2−(−2))+(−3)(−2−3)∣

=21​∣1(1)+2(4)+(−3)(−5)∣

=21​∣1+8+15∣

=224​=12 sq. units

ar(ABCD) parallelogram =2× Area of triangle

=2×12

=24 sq. units

Area of parallelogram =Base × Height

BaseArea​=height

So by the distance formula

=(x2​−x1​)2+(y2​−y1​)2​

=(−3+4)2+(2+3)2​

=1+25​

=26​

Thus height =26​24​=26​24​×26​26​​=262426​​=131226​​.

Step-by-step explanation: