The vector is first dilated by a factor of 2.5 and then rotated by radians. If the resulting vector is , then a =_ and b = _.

a = 10

b = 2.5

Step-by-step explanation:

The given vector is

<-1, 4>

Let represents <-1, 4>.

First, the dilation is done by a factor of 2.5.

If the dilation of a vector <, > is done by a factor k:

Then the resulting vector becomes:

The resulting as per above explanation:

Now, it is given that the vector is rotated by or .

The steps to find the resulting vector after the rotation of or , we can use the simple method:

Step 1:  Multiply the value with -1.

i.e. the vector now becomes <2.5, 10> (Negative sign of x value removed).

Step 2: Swap the values of and .

So, the resulting vector is:

<10, 2.5>

In other form, we can represent the above vector as:

Comparing with

a = 10

b = 2.5

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.