Midpoint Formula 2
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Question 1 of 7
1. Question
Find the midpoint of the line segment with the given endpoints `A(7,3)` and `B(−5,10)`. Give your answer in decimals, if necessary.
- `\text(Midpoint) =` (1), (6.5)
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Midpoint Formula
$$\text{Midpoint}=m=(\frac{\color{#9202AA}{x_1+x_2}}{2},\frac{\color{#00880A}{y_1+y_2}}{2})$$First, label the given coordinates`A(``7``,``3``) = A(``x_1``,``y_1``)``B(``-5``,``10``) = B(``x_2``,``y_2``)`Solve using the Midpoint Formula`m` `=` $$(\frac{\color{#9202AA}{x_1+x_2}}{2},\frac{\color{#00880A}{y_1+y_2}}{2})$$ Midpoint Formula `=` $$(\frac{\color{#9202AA}{7+(-5)}}{2},\frac{\color{#00880A}{3+10}}{2})$$ Plug in the coordinates `=` `(2/2,13/2)` Simplify `=` `(1,6.5)` `\text(Midpoint) =(1,6.5)`
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Question 2 of 7
2. Question
Find the coordinates of point `M` if `A` is at `(1,2)` and `B` is at `(5,6)`
- `\text(M) =(` (3), (4)`)`
Hint
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Midpoint Formula
$$\text{Midpoint}=m=(\frac{\color{#9202AA}{x_1+x_2}}{2},\frac{\color{#00880A}{y_1+y_2}}{2})$$First, label the given coordinates`A(``1``,``2``) = A(``x_1``,``y_1``)``B(``5``,``6``) = B(``x_2``,``y_2``)`Solve using the Midpoint Formula`m` `=` $$(\frac{\color{#9202AA}{x_1+x_2}}{2},\frac{\color{#00880A}{y_1+y_2}}{2})$$ Midpoint Formula `=` $$(\frac{\color{#9202AA}{1+5}}{2},\frac{\color{#00880A}{2+6}}{2})$$ Plug in the coordinates `=` `(6/2,8/2)` Simplify `=` `(3,4)` `\text(Midpoint) =(3,4)`
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Question 3 of 7
3. Question
Find the midpoint between the points `A(-4,-2)` and `B(2,4)`
- Midpoint`=` (-1), (1)
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Midpoint Formula
`M=((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))`First, label the given coordinates`A(color(darkviolet)(-4),color(forestgreen)(-2))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(2),color(forestgreen)(4))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))`Solve using the Midpoint FormulaMidpoint `=` `((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))` Midpoint Formula `=` `((color(darkviolet)(-4+2))/(2),(color(forestgreen)(-2+4))/(2))` Plug in the coordinates `=` `((-2)/(2),2/2)` Simplify `=` `(-1,1)` Midpoint`=(-1,1)` -
Question 4 of 7
4. Question
Find the midpoint between the points `A(-1,3)` and `B(8,-5)`
- Midpoint`=` (3.5), (-1)
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Midpoint Formula
`M=((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))`First, label the given coordinates`A(color(darkviolet)(-1),color(forestgreen)(3))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(8),color(forestgreen)(-5))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))`Solve using the Midpoint FormulaMidpoint `=` `((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))` Midpoint Formula `=` `((color(darkviolet)(-1+8))/(2),(color(forestgreen)(3+(-5)))/(2))` Plug in the coordinates `=` `(7/2,(-2)/2)` Simplify `=` `(3.5,-1)` Midpoint`=(3.5,-1)` -
Question 5 of 7
5. Question
Find the midpoint between the points `A(3,-2)` and `B(6,2)`
- Midpoint`=` (4.5), (0)
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Midpoint Formula
`M=((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))`First, label the given coordinates`A(color(darkviolet)(3),color(forestgreen)(-2))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(6),color(forestgreen)(2))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))`Solve using the Midpoint FormulaMidpoint `=` `((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))` Midpoint Formula `=` `((color(darkviolet)(3+6))/(2),(color(forestgreen)(-2+2))/(2))` Plug in the coordinates `=` `(9/2,0/2)` Simplify `=` `(4.5,0)` Midpoint`=(4.5,0)` -
Question 6 of 7
6. Question
Find the midpoint between the points `A(6,2)` and `B(3,-2)`
- Midpoint`=` (4.5), (0)
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Midpoint Formula
`M=((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))`First, label the given coordinates`A(color(darkviolet)(6),color(forestgreen)(2))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(3),color(forestgreen)(-2))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))`Solve using the Midpoint FormulaMidpoint `=` `((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))` Midpoint Formula `=` `((color(darkviolet)(6+3))/(2),(color(forestgreen)(2-2))/(2))` Plug in the coordinates `=` `(9/(2),0/2)` Simplify `=` `(4.5,0)` Midpoint`=(4.5,0)` -
Question 7 of 7
7. Question
Given the midpoint `M(4,4)` and one endpoint `A(-10,-2)` of a line segment, find the other endpoint `B \text((Unknown))`
- `\text(B) =(` (18), (10)`)`
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Midpoint Formula
$$\text{Midpoint}=m=(\frac{\color{#9202AA}{x_1+x_2}}{2},\frac{\color{#00880A}{y_1+y_2}}{2})$$First, label the given coordinates`A(``-10``,``-2``) = A(``x_1``,``y_1``)``m=(4,4)`Substitute the values into the Midpoint Formula`m` `=` $$(\frac{\color{#9202AA}{x_1+x_2}}{2},\frac{\color{#00880A}{y_1+y_2}}{2})$$ Midpoint Formula `=` $$(4,4)=(\frac{\color{#9202AA}{-10+x_2}}{2},\frac{\color{#00880A}{-2+y_2}}{2})$$ Plug in the coordinates Solve for each coordinate individually$$4$$ `=` $$\frac{\color{#9202AA}{-10+x_2}}{2}$$ $$8$$ `=` $$\color{#9202AA}{-10+x_2}$$ $$\color{#9202AA}{18}$$ `=` $$\color{#9202AA}{x_2}$$ $$\color{#9202AA}{x_2}$$ `=` $$\color{#9202AA}{18}$$ $$4$$ `=` $$\frac{\color{#00880A}{-2+y_2}}{2}$$ $$8$$ `=` $$\color{#00880A}{-2+y_2}$$ $$\color{#00880A}{10}$$ `=` $$\color{#00880A}{y_2}$$ $$\color{#00880A}{y_2}$$ `=` $$\color{#00880A}{10}$$ Combine obtained values`B=(``x_2``,``y_2``) = B(``18``,``10``)``\text(B) =(18,10)`