Question

points A(3,1) ;B(5,1); C(a,b) and D(4,3)are vertices of a parallelogram ABCD .find the values of a and b​

Answer 1

$\large\bold{ \underline{ \underline{ \: Answer : \: \: \: }}}$

$\to$ a = 6

$\to$ b = 3

$\large\bold{ \underline{ \underline{ \: Explanation : \: \: \: }}}$

Mid point of AC = Mid point of BD

Mid point = $( \bold{ \frac{X_{1} \: + \: X_{2}}{2} \: , \: \frac{Y_{1} \: + \: Y _{2}}{2} })$

According to the question ,

$\to ( \frac{3 \: + \: a}{2} , \frac{1 \: + \: b}{2}) =( \frac{5 \: + \: 4}{2} , \frac{1 \: + \: 3}{2} )$

$\large \bold{ \underline{ \: \: For \: finding \: the \: value \: of \: a \: \: \: }}$

$\to \frac{3 + a}{2} = \frac{5 + 4}{2} \\ \\ \to 3+a=5+4 \\ \ \\ \to a = 9-3 \\ \\ \to a=6$

$\large \bold{ \underline{ \: \: For \: finding \: the \: value \: of \: b \: \: \: }}$

$\to \frac{1 + b}{2} = \frac{1 + 3}{2} \\ \\ \to</p><p>1+b=1+3</p><p> \\ \\ \to</p><p>b= 4-1</p><p> \\ \\ \to</p><p>b= 3</p><p>$

Therefore , a = 6 and b = 3