Question

On a parallelogram, the vector from one vertex to another vertex is (9,-2). What is the length of the side?

Answer 1

Answer:

The length of the side of the parallelogram is $\sqrt{85}$.

Step-by-step explanation:

It is given that the vector from one vertex to another vertex is (9,-2), thus we can write it in the vector from that is $v=9\hat{i}+(-2)\hat{j}$ and let the another vertex is adjacent to it.

Now, in order to find the length of the side of the parallelogram, we use the absolute modulus that is $|v|=\sqrt{a^{2}+b^{2}}$.

Now, since v=(9,-2), thus $|v|=\sqrt{(9)^{2}+(-2)^{2}}$

=$\sqrt{81+4}$

=$\sqrt{85}$

Thus, the length of the side of the parallelogram is $\sqrt{85}$.

Answer 2

Answer:  Second Option is correct.

Step-by-step explanation:

Since we have given that

In a parallelogram, the vector from one vertex to another vertex is (9,-2)

So, the co-ordinate of first vertex will be (9,0).

And the coordinate of second vertex will be (0,-2).

As we know the formula for "Distance between two coordinates":

So, The length of the side is given by

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\Distance=\sqrt{(9-0)^2+(0-(-2))^2}\\\\Distance=\sqrt{9^2+2^2}\\\\Distance=\sqrt{81+4}\\\\Distance=\sqrt{85}$

Hence, Second Option is correct.