Question

If the points A(6,1) B(8,2), C(9,4), D(p,4) are the vertices of parallelogram. Find the value of p.

Answer 1

Answer:

$9 \pm \sqrt{5}$

Step-by-step explanation:

We have parallelogram with sides A(6,1) B(8,2) C(9,4) D(p,4).

Since ABCD is a parallelogram, so sides AB and CD have same length. So AB = CD.

By using distance formula we get:

${(6 - 8)}^{2} + {(1 - 2)}^{2} = {(9 - p)}^{2} + {(4 - 4)}^{2}$

On further solving we get:

${2}^{2} + {1}^{2} = {(9 - p)}^{2}$

And finally:

$p =9 \pm \sqrt{5}$