Question

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

•7
•√85
•18
•85

Answer 1

The length of the side of the parallelogram is
`√(85)`.

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)}`

=
`√(81+4)`

=
`√(85)`

Thus, the length of the side of the parallelogram is
`√(85)`.

Answer 2

Answer: Second Option is correct.

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=√((x_2-x_1)^2+(y_2-y_1)^2)\\\\Distance=√((9-0)^2+(0-(-2))^2)\\\\Distance=√(9^2+2^2)\\\\Distance=√(81+4)\\\\Distance=√(85)`

Hence, Second Option is correct.