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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 39 Page 706

The component form of a vector is ⟨ x_2-x_1,y_2-y_1 ⟩.

⟨ - 6,- 5 ⟩

Practice makes perfect

We use the component form of a vector to describe the vector in terms of its horizontal component x and vertical component y. ⟨ x,y ⟩

To write the component form of a vector with initial point (x_1,y_1) and terminal point (x_2,y_2), we need to find ⟨ x_2-x_1,y_2-y_1 ⟩. Let's identify the initial and terminal points of the given vector. Remember, the initial point is written as a dot, while the terminal point is shown as an arrow.

Now, we can substitute these values into the component form of a vector and simplify.

AB = ⟨ x_2-x_1,y_2-y_1 ⟩

SubstitutePoints

Substitute ( 5,2) & ( -1,-3)

AB = ⟨ - 1- 5, - 3- 2 ⟩

Subtract terms

AB = ⟨ -6,-5 ⟩

Subchapter links

1 Geometric Mean p.703

2 The Pythagorean Theorem and Its Converse p.703

3 Special Right Triangles p.704

4 Trigonometry p.704

5 Angles of Elevation and Depression p.705

6 The Law of Sines and Law of Cosines p.705

7 Vectors p.706

8 Dilations p.706