Vector Components from Initial and Terminal Points

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

In this learning activity, students will learn how to find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. This learning activity can be used as a stand-alone activity or a core lesson activity. Corresponding activities can be found in the Notes or Recommendations section.

Phase

During/Explore/Explain

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.9
Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

Vocabulary

Components
Initial Point
Terminal Point

Knowledge

Students know:

If a vector is transposed in the xy-plane, it retains its magnitude and direction.

Skills

Students are able to:

Transpose a vector from one position to another position in the xy-plane.
Find the component form of a vector.

Understanding

Students understand that:

Vectors having the same magnitude and direction are equivalent regardless of where they are in the xy-plane.
Vectors in standard position have a terminal point that is equal to the components of the vector.

Learning Objectives

Students will be able to:

describe a set of components in terms of the numbers of units right/left and up/down, and vice versa.
identify the initial and terminal points of a vector.
understand the relation between vector components and initial and terminal points.

Activity Details

Procedure

1. Introduction (5 minutes, whole group)
The teacher will review the component form of a vector: (The teacher can skip this step if he/she used the Before Activity.)

Remind the students that the component form of a vector is given as < x, y >, where x describes how far right or left a vector is going and y describes how far up or down a vector is going.
Given a vector’s initial point (where it starts), (x₁, y₁), and terminal point (where it ends), (x₂, y₂) the component form can be found by subtracting the coordinates of each point: < x₂ – x₁, y₂ – y₁ >.

2. Watching the Video (10 minutes, whole group):

The teacher will show the teaching video.

3. Conclusion (10 minutes, whole group)

The teacher will display the following problems to be worked on as a whole group to check for understanding.

- 1. Find the component form of the vector with initial point <d,e> and terminal point <f,g>.
- 2. Find the component form of the vector with initial point <0,1> and terminal point <4,5>.
- 3. Find the component form of the vector with initial point <-5,-9> and terminal point <-6,-11>.
- 4. Find the component form of the vector with initial point <3,8> and terminal point <-3,-8>.

The teacher will assign additional problems to be worked on with a partner to check for understanding.

Assessment Strategies

The student responses during the class discussion and additional problems will be used as a formative assessment.

Variation Tips

- For students who struggle with this activity, the teacher should provide a work buddy.
- For students who excel at this activity, the teacher could assign the example problems individually.
- The teacher can assign the additional problems to be worked on individually instead of with a partner.

Background / Preparation

- Students should already be familiar with finding the coordinates of a point on a coordinate plane.
- The teacher should review the teaching video prior to the lesson.
- The teacher will need to decide how he/she will display the video and the problems to check for understanding.

- The teacher will need to decide how he/she wants to digitally assign the additional problems.

Vector magnitude from initial & terminal points from Khan Academy

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f…

Approved Date

2022-06-28

Owner (Author)

yvetteakridge

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