Common Core: High School - Number and Quantity : Vector & Matrix Quantities

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

varsity tutors app store varsity tutors android store

All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Vector & Matrix Quantities

Vector \displaystyle \vec{w}, has an initial point of \displaystyle (-3, 5), and a terminal point of \displaystyle (5,6). What is the slope of vector \displaystyle \vec{w}?

Possible Answers:

\displaystyle -\frac{1}{8}

\displaystyle 8

\displaystyle \frac{1}{4}

\displaystyle \frac{1}{8}

\displaystyle -2

Correct answer:

\displaystyle \frac{1}{8}

Explanation:

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in \displaystyle y coordinates over the change in \displaystyle x coordinates. In equation form it looks like 

\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}, where \displaystyle y_2, y_1 are the \displaystyle y coordinates, and \displaystyle x_2, x_1 are the \displaystyle x coordinates.

For this example, we will let \displaystyle y_2=6, y_1=5, x_2=5, x_1=-3.

\displaystyle \mbox{Slope}=\frac{6-5}{5-(-3)}=\frac{1}{5+3}=\frac{1}{8}

 

Below is a visual representation of what we just did. The orange arrow is \displaystyle \vec{w}.

 Vector

Example Question #2 : Vector & Matrix Quantities

Vector \displaystyle \vec{w}, has an initial point of \displaystyle (-6, 3), and a terminal point of \displaystyle (2,6). What is the slope of vector \displaystyle \vec{w}?

Possible Answers:

\displaystyle \frac{8}{3}

\displaystyle \frac{3}{8}

\displaystyle 8

\displaystyle -\frac{3}{8}

\displaystyle 3

Correct answer:

\displaystyle \frac{3}{8}

Explanation:

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in \displaystyle y coordinates over the change in \displaystyle x coordinates. In equation form it looks like 

\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}, where \displaystyle y_2, y_1 are the \displaystyle y coordinates, and \displaystyle x_2, x_1 are the \displaystyle x coordinates.

For this example, we will let \displaystyle y_2=6, y_1=3, x_2=2, x_1=-6.

\displaystyle \mbox{Slope}=\frac{6-3}{2-(-6)}=\frac{3}{2+6}=\frac{3}{8}

 

Below is a visual representation of what we just did. The orange arrow is \displaystyle \vec{w}.

 

Slope2

Example Question #2 : Vector & Matrix Quantities

Vector \displaystyle \vec{w}, has an initial point of \displaystyle (2, 11), and a terminal point of \displaystyle (-3,-7). What is the slope of vector \displaystyle \vec{w}?

Possible Answers:

\displaystyle \frac{5}{18}

\displaystyle -\frac{18}{5}

\displaystyle -18

\displaystyle -\frac{5}{18}

\displaystyle \frac{18}{5}

Correct answer:

\displaystyle \frac{18}{5}

Explanation:

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in \displaystyle y coordinates over the change in \displaystyle x coordinates. In equation form it looks like 

\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}, where \displaystyle y_2, y_1 are the \displaystyle y coordinates, and \displaystyle x_2, x_1 are the \displaystyle x coordinates.

For this example, we will let \displaystyle y_2=-7, y_1=11, x_2=-3, x_1=2.

\displaystyle \mbox{Slope}=\frac{-7-11}{-3-2}=\frac{-18}{-5}=\frac{18}{5}

 

Below is a visual representation of what we just did. The orange arrow is \displaystyle \vec{w}.

Slope3

Example Question #1 : Vector & Matrix Quantities

Vector \displaystyle \vec{w}, has an initial point of \displaystyle (5, -3), and a terminal point of \displaystyle (6,5). What is the slope of vector \displaystyle \vec{w}?

Possible Answers:

\displaystyle 8

\displaystyle 18

\displaystyle -\frac{1}{8}

\displaystyle -8

\displaystyle \frac{1}{8}

Correct answer:

\displaystyle 8

Explanation:

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in \displaystyle y coordinates over the change in \displaystyle x coordinates. In equation form it looks like 

\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}, where \displaystyle y_2, y_1 are the \displaystyle y coordinates, and \displaystyle x_2, x_1 are the \displaystyle x coordinates.

For this example, we will let \displaystyle y_2=5, y_1=-3, x_2=6, x_1=5.

\displaystyle \mbox{Slope}=\frac{5-(-3)}{6-5}=\frac{5+3}{1}=\frac{8}{1}=8

 

Below is a visual representation of what we just did. The orange arrow is \displaystyle \vec{w}.

 

Slope4

Example Question #3 : Vector & Matrix Quantities

Vector \displaystyle \vec{w}, has an initial point of \displaystyle (15, 6), and a terminal point of \displaystyle (-7,1). What is the slope of vector \displaystyle \vec{w}?

Possible Answers:

\displaystyle 5

\displaystyle 22

\displaystyle \frac{5}{22}

\displaystyle -\frac{5}{22}

\displaystyle \frac{22}{5}

Correct answer:

\displaystyle \frac{5}{22}

Explanation:

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in \displaystyle y coordinates over the change in \displaystyle x coordinates. In equation form it looks like 

\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}, where \displaystyle y_2, y_1 are the \displaystyle y coordinates, and \displaystyle x_2, x_1 are the \displaystyle x coordinates.

For this example, we will let \displaystyle y_2=1, y_1=6, x_2=-7, x_1=15.

\displaystyle \mbox{Slope}=\frac{1-6}{-7-15}=\frac{-5}{-22}=\frac{5}{22}

 

Below is a visual representation of what we just did. The orange arrow is \displaystyle \vec{w}.

 

Slope5

Example Question #5 : Vector Magnitude And Direction: Ccss.Math.Content.Hsn Vm.A.1

Vector \displaystyle \vec{w}, has an initial point of \displaystyle (3, 2), and a terminal point of \displaystyle (-3,5). What is the slope of vector \displaystyle \vec{w}?

Possible Answers:

\displaystyle 2

\displaystyle -\frac{1}{2}

\displaystyle \frac{1}{2}

\displaystyle -2

\displaystyle 1

Correct answer:

\displaystyle -\frac{1}{2}

Explanation:

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in \displaystyle y coordinates over the change in \displaystyle x coordinates. In equation form it looks like 

\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}, where \displaystyle y_2, y_1 are the \displaystyle y coordinates, and \displaystyle x_2, x_1 are the \displaystyle x coordinates.

For this example, we will let \displaystyle y_2=5, y_1=2, x_2=-3, x_1=3.

\displaystyle \mbox{Slope}=\frac{5-2}{-3-3}=\frac{3}{-6}=-\frac{1}{2}

 

Below is a visual representation of what we just did. The orange arrow is \displaystyle \vec{w}.

 

Slope6

Example Question #3 : Vector & Matrix Quantities

Vector \displaystyle \vec{w}, has an initial point of \displaystyle (-3, -5), and a terminal point of \displaystyle (-5,6). What is the slope of vector \displaystyle \vec{w}?

Possible Answers:

\displaystyle \frac{2}{11}

\displaystyle 2

\displaystyle -\frac{2}{11}

\displaystyle \frac{11}{2}

\displaystyle -\frac{11}{2}

Correct answer:

\displaystyle -\frac{11}{2}

Explanation:

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in \displaystyle y coordinates over the change in \displaystyle x coordinates. In equation form it looks like 

\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}, where \displaystyle y_2, y_1 are the \displaystyle y coordinates, and \displaystyle x_2, x_1 are the \displaystyle x coordinates.

For this example, we will let \displaystyle y_2=6, y_1=-5, x_2=-5, x_1=-3.

\displaystyle \mbox{Slope}=\frac{6-(-5)}{-5-(-3)}=\frac{6+5}{-5+3}=\frac{11}{-2}=-\frac{11}{2}

 

Below is a visual representation of what we just did. The orange arrow is \displaystyle \vec{w}.

 


Slope7

Example Question #2 : Vector & Matrix Quantities

Vector \displaystyle \vec{w}, has an initial point of \displaystyle (-20, 15), and a terminal point of \displaystyle (0,-8). What is the slope of vector \displaystyle \vec{w}?

Possible Answers:

\displaystyle 23

\displaystyle \frac{20}{23}

\displaystyle -\frac{20}{23}

\displaystyle \frac{23}{20}

\displaystyle -\frac{23}{20}

Correct answer:

\displaystyle \frac{23}{20}

Explanation:

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in \displaystyle y coordinates over the change in \displaystyle x coordinates. In equation form it looks like 

\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}, where \displaystyle y_2, y_1 are the \displaystyle y coordinates, and \displaystyle x_2, x_1 are the \displaystyle x coordinates.

For this example, we will let \displaystyle y_2=-8, y_1=15, x_2=0, x_1=-20.

\displaystyle \mbox{Slope}=\frac{15-(-8)}{0-(-20)}=\frac{15+8}{0+20}=\frac{23}{20}

 

Below is a visual representation of what we just did. The orange arrow is \displaystyle \vec{w}.

 

Slope8

Example Question #1 : Vector & Matrix Quantities

Vector \displaystyle \vec{w}, has an initial point of \displaystyle (0, 2), and a terminal point of \displaystyle (2,7). What is the slope of vector \displaystyle \vec{w}?

Possible Answers:

\displaystyle -\frac{2}{5}

\displaystyle -\frac{5}{2}

\displaystyle \frac{5}{2}

\displaystyle \frac{2}{5}

\displaystyle 2

Correct answer:

\displaystyle \frac{5}{2}

Explanation:

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in \displaystyle y coordinates over the change in \displaystyle x coordinates. In equation form it looks like 

\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}, where \displaystyle y_2, y_1 are the \displaystyle y coordinates, and \displaystyle x_2, x_1 are the \displaystyle x coordinates.

For this example, we will let \displaystyle y_2=7, y_1=2, x_2=2, x_1=0.

\displaystyle \mbox{Slope}=\frac{7-2}{2-0}=\frac{5}{2}

 

Below is a visual representation of what we just did. The orange arrow is \displaystyle \vec{w}.

Slope9

Example Question #4 : Vector & Matrix Quantities

Vector \displaystyle \vec{w}, has an initial point of \displaystyle (2, -10), and a terminal point of \displaystyle (8,-1). What is the slope of vector \displaystyle \vec{w}?

Possible Answers:

\displaystyle \frac{3}{2}

\displaystyle \frac{2}{3}

\displaystyle -\frac{3}{2}

\displaystyle -2

\displaystyle -\frac{2}{3}

Correct answer:

\displaystyle \frac{3}{2}

Explanation:

In order to figure out slope, we need to remember how to find slope. Slope can be found be doing rise over run, or simply the change in \displaystyle y coordinates over the change in \displaystyle x coordinates. In equation form it looks like 

\displaystyle \mbox{Slope}=\frac{y_2-y_1}{x_2-x_1}, where \displaystyle y_2, y_1 are the \displaystyle y coordinates, and \displaystyle x_2, x_1 are the \displaystyle x coordinates.

For this example, we will let \displaystyle y_2=-1, y_1=-10, x_2=8, x_1=2.

\displaystyle \mbox{Slope}=\frac{-1-(-10)}{8-2}=\frac{-1+10}{8-2}=\frac{9}{6}=\frac{3}{2}

 

Below is a visual representation of what we just did. The orange arrow is \displaystyle \vec{w}.


Slope10

All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept
Learning Tools by Varsity Tutors