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Common Core: High School - Number and Quantity : Vector Magnitude and Direction: CCSS.Math.Content.HSN-VM.A.1

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

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Example Questions

Example Question #1 : Vector & Matrix Quantities

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

Possible Answers:

$-\frac{1}{8}$

$\frac{1}{8}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{8}$

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 coordinates over the change in coordinates. In equation form it looks like

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

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

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

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

Vector

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Example Question #2 : Vector Magnitude And Direction: Ccss.Math.Content.Hsn Vm.A.1

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

Possible Answers:

$\frac{8}{3}$

$-\frac{3}{8}$

$\frac{3}{8}$

Correct answer:

$\frac{3}{8}$

Explanation:

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

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

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

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

Slope2

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Example Question #1 : Vector & Matrix Quantities

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

Possible Answers:

$\frac{18}{5}$

$\frac{5}{18}$

$-\frac{5}{18}$

$-\frac{18}{5}$

Correct answer:

$\frac{18}{5}$

Explanation:

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

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

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

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

Slope3

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Example Question #2 : Vector & Matrix Quantities

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

Possible Answers:

$\frac{1}{8}$

$-\frac{1}{8}$

Correct answer:

Explanation:

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

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

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

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

Slope4

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Example Question #3 : Vector & Matrix Quantities

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

Possible Answers:

$\frac{5}{22}$

$-\frac{5}{22}$

$\frac{22}{5}$

Correct answer:

$\frac{5}{22}$

Explanation:

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

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

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

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

Slope5

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

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

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

$-\frac{1}{2}$

Explanation:

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

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

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

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

Slope6

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Example Question #1 : Vector & Matrix Quantities

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

Possible Answers:

$\frac{2}{11}$

$-\frac{11}{2}$

$\frac{11}{2}$

$-\frac{2}{11}$

Correct answer:

$-\frac{11}{2}$

Explanation:

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

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

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

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

Slope7

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Example Question #3 : Vector & Matrix Quantities

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

Possible Answers:

$\frac{23}{20}$

$-\frac{20}{23}$

$-\frac{23}{20}$

$\frac{20}{23}$

Correct answer:

$\frac{23}{20}$

Explanation:

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

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

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

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

Slope8

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Example Question #4 : Vector & Matrix Quantities

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

Possible Answers:

$-\frac{2}{5}$

$\frac{2}{5}$

$\frac{5}{2}$

$-\frac{5}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

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

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

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

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

Slope9

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Example Question #4 : Vector & Matrix Quantities

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

Possible Answers:

$\frac{3}{2}$

$\frac{2}{3}$

$-\frac{3}{2}$

$-\frac{2}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

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

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

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

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

Slope10

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Common Core: High School - Number and Quantity : Vector Magnitude and Direction: CCSS.Math.Content.HSN-VM.A.1

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

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #1 : Vector & Matrix Quantities

Example Question #2 : Vector Magnitude And Direction: Ccss.Math.Content.Hsn Vm.A.1

Example Question #1 : Vector & Matrix Quantities

Example Question #2 : Vector & Matrix Quantities

Example Question #3 : Vector & Matrix Quantities

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

Example Question #1 : Vector & Matrix Quantities

Example Question #3 : Vector & Matrix Quantities

Example Question #4 : Vector & Matrix Quantities

Example Question #4 : Vector & Matrix Quantities

All Common Core: High School - Number and Quantity Resources

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