Question

Identify the ordered pair that represents the vector from a(-9 9) to b(7 3) and the magnitude of AB

Answer 1

Answer: 17.09

Step-by-step explanation:

Given:  The ordered pair that represents the vector from A(-9 9) to B(7 3).

The length of vector from points $(x_1,y_1)$ and  $(x_2,y_2)$  is given by  using distance formula:-

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Now, the length of vector AB is given by:-

$AB=\sqrt{(7-(-9))^2+(3-9)^2}\\\\=\sqrt{(7+9)^2+(-6)^2}\\\\=\sqrt{(16^2)+36} \\\\=\sqrt{256+36} \\\\=\sqrt{292}=17.0880074906\approx17.09$

Therefore, the magnitude of Ab = 17.09

Answer 2

Moving from a to b, the x component  of the desired vector is 7-(-9) = 16, and
the y component is 3-9 = -6.

So the vector from a to b is <16,-6>, and the magnitude is

sqrt(16^2 + (-6)^2 ), applying the Pythagorean Theorem.