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Common Core: High School - Number and Quantity : High School: Number and Quantity

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

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All Common Core: High School - Number and Quantity Resources

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Example Questions

Example Question #11 : Vector & Matrix Quantities

What are the components of a vector that has a terminal point of (1,1) , and an initial point of (-6,-9) ?

Possible Answers:

<0,0>

<7,10>

<-10,-7>

<-7,-10>

<10,7>

Correct answer:

<7,10>

Explanation:

In order to determine what the components of this vector has, we need to remember how to find components of a vector. It's simply the difference between the terminal point and initial point. The first step is to write an equation for what our "new" x and y are.

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=1 \\ \mbox{(x in initial point)}=-6 \\ \mbox{(y in terminal point)}=1\\ \mbox{(y in initial point)}= -9$

x=1-(-6)=1+6=7

y=1-(-9)=1+9=10

To write this in component form, we need to put our , and into .

So the final answer is <7,10>

Below is a visual representation of what we just did.

Screen shot 2016 03 15 at 10.39.47 am

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Example Question #12 : Vector & Matrix Quantities

What are the components of a vector that has a terminal point of (-9,1) , and an initial point of (5,-10) ?

Possible Answers:

<-14,11>

<14,-11>

<11,-14>

<11,14>

<-14,-11>

Correct answer:

<-14,11>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=-9 \\ \mbox{(x in initial point)}=2 \\ \mbox{(y in terminal point)}=1\\ \mbox{(y in initial point)}= -10$

x=-9-5=-14

y=1-(-10)=1+10=11

To write this in component form, we need to put our , and into .

So the final answer is <-14,11>

Below is a visual representation of what we just did.

Screen shot 2016 03 15 at 10.52.08 am

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Example Question #113 : High School: Number And Quantity

What are the components of a vector that has a terminal point of (3,-8) , and an initial point of (6,-13) ?

Possible Answers:

<-21,9>

<9,-21>

<-3,5>

<5,-3>

<-5,-7>

Correct answer:

<-3,5>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=3 \\ \mbox{(x in initial point)}=6 \\ \mbox{(y in terminal point)}=-8\\ \mbox{(y in initial point)}= -13$

x=3-6=-3

y=-8-(-13)=-8+13=5

To write this in component form, we need to put our , and into .

So the final answer is <-3,5>

Below is a visual representation of what we just did.

Screen shot 2016 03 15 at 12.32.48 pm

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Example Question #114 : High School: Number And Quantity

What are the components of a vector that has a terminal point of (-1,-5) , and an initial point of (-4,-9) ?

Possible Answers:

<-4,3>

<8,-1>

<4,5>

<4,3>

<3,4>

Correct answer:

<3,4>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=-1 \\ \mbox{(x in initial point)}=-4 \\ \mbox{(y in terminal point)}=-5\\ \mbox{(y in initial point)}= -9$

x=-1-(-4)=-1+4=3

y=-5-(-9)=-5+9=4

To write this in component form, we need to put our , and into .

So the final answer is <3,4>

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 12.09.51 pm

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Example Question #3 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (-3,10) , and an initial point of (-4,12) ?

Possible Answers:

<1,2>

<-2,1>

<1,-2>

<-15,14>

<14,-15>

Correct answer:

<1,-2>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=-3 \\ \mbox{(x in initial point)}=-4 \\ \mbox{(y in terminal point)}=10\\ \mbox{(y in initial point)}=12$

x=-3-(-4)=-3+4=1

y=10-12=-2

To write this in component form, we need to put our , and into .

So the final answer is <1,-2>

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 12.32.22 pm

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Example Question #4 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (1,9) , and an initial point of (-7,5) ?

Possible Answers:

<8,4>

<8,14>

<4,-6>

<-6,4>

<4,6>

Correct answer:

<8,4>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=1 \\ \mbox{(x in initial point)}=-7 \\ \mbox{(y in terminal point)}=9\\ \mbox{(y in initial point)}= 5$

x=1-(-7)=1+7=8

y=9-5=4

To write this in component form, we need to put our , and into .

So the final answer is <8,4>

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 12.41.19 pm

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Example Question #1 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (4,6) , and an initial point of (0,-8) ?

Possible Answers:

<6,12>

<-2,8>

<12,6>

<14,4>

<4,14>

Correct answer:

<4,14>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=4 \\ \mbox{(x in initial point)}=0 \\ \mbox{(y in terminal point)}=6\\ \mbox{(y in initial point)}= -8$

x=4-0=4

y=6-(-8)=6+8=14

To write this in component form, we need to put our , and into .

So the final answer is <4,14>

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 1.16.38 pm

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Example Question #5 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (3,-6) , and an initial point of (10,5) ?

Possible Answers:

<-11,-7>

<-7,-11>

<-8,4>

<8,4>

<8,-4>

Correct answer:

<-7,-11>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=3 \\ \mbox{(x in initial point)}=10 \\ \mbox{(y in terminal point)}=-6\\ \mbox{(y in initial point)}=5$

x=3-10=-7

y=-6-5=-11

To write this in component form, we need to put our , and into .

So the final answer is <-7,-11>

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 1.27.32 pm

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Example Question #11 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (-6,10) , and an initial point of (-9,11) ?

Possible Answers:

<1,-5>

<3,-1>

<-1,3>

<-16,-20>

<-17,19>

Correct answer:

<3,-1>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=-6 \\ \mbox{(x in initial point)}=-9 \\ \mbox{(y in terminal point)}=10\\ \mbox{(y in initial point)}= 11$

x=-6-(-9)=-6+9=3

y=10-11=-1

To write this in component form, we need to put our , and into .

So the final answer is <3,-1>

Below is a visual representation of what we just did.

Screen shot 2016 03 16 at 1.33.55 pm

Report an Error

Example Question #12 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

What are the components of a vector that has a terminal point of (1,3) , and an initial point of (3,1) ?

Possible Answers:

<-2,2>

<2,-2>

<2,2>

<-2,-2>

<-2,0>

Correct answer:

<-2,2>

Explanation:

$x=\mbox{(x in terminal point)}-\mbox{(x in initial point) }$

$y=\mbox{(y in terminal point)}-\mbox{(y in initial point) }$

Now lets identify what these values are.

$\\ \mbox{(x in terminal point)}=1 \\ \mbox{(x in initial point)}=3 \\ \mbox{(y in terminal point)}=3\\ \mbox{(y in initial point)}= 1$

x=1-3=-2

y=3-1=2

To write this in component form, we need to put our , and into .

So the final answer is <-2,2>

Below is a visual representation of what we just did.

Comp3

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All Common Core: High School - Number and Quantity Resources

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Common Core: High School - Number and Quantity : High School: Number and Quantity

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 #11 : Vector & Matrix Quantities

Example Question #12 : Vector & Matrix Quantities

Example Question #113 : High School: Number And Quantity

Example Question #114 : High School: Number And Quantity

Example Question #3 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

Example Question #4 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

Example Question #1 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

Example Question #5 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

Example Question #11 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

Example Question #12 : Vector Components: Ccss.Math.Content.Hsn Vm.A.2

All Common Core: High School - Number and Quantity Resources

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