Question

if the points A(6 ,1) B (8,2) C (p,4) D(7,3) are the vertices of parallelogram taken in order, find the value of p​

Answer 1

Answer:

9

Step-by-step explanation:

Sides of parallelogram are parallel.

It implies, slope of AB = slope of CD.

=> (2 - 1)/(8 - 6) = (4 - 3)/(p - 7)

=> 1/2 = 1/(p - 7)

=> 1(p - 7) = 2

=> p - 7 = 2

=> p = 2 + 7

=> p = 9

You can use the slopes of AD and BC.

=> (3 - 1)/(7 - 6)= (4 - 2)/(p - 8)

=> 2/1 = 2/(p - 8)

=> (p - 8) = 1

=> p = 8 + 1

=> p = 9

Answer 2

Solution :

we know that,

• Opposite sides of parallelogram are equal.

So,

• Slope AB = Slope DC

$\sf : \implies \: \frac{y _2 - y _1}{x_2 - x_1 } = \frac{y _2 - y _1}{x_2 - x_1 } \\ \\ \sf : \implies \: \frac{(2 - 1)}{(8 - 6)} = \frac{(4 - 3)}{(p - 7)} \\ \\ \sf : \implies \: \frac{1}{2} = \frac{1}{(p - 7)} \\ \\ \sf : \implies \:p - 7 = 2 \\ \\ \sf : \implies \:p = 2 + 7 \\ \\ \sf \boxed{ \sf \: p = 9}$

Hence

• value of p is 9

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