Midpoint of a Line 1
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Question 1 of 7
1. Question
Find the midpoint of `PQ` if `P(1,6)` and `Q(5,0)`
Hint
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Midpoint Formula
$$\text{Midpoint}=m=(\frac{\color{#7d02aa}{x_1+x_2}}{2},\frac{\color{#00880a}{y_1+y_2}}{2})$$First, label the given coordinates`P(``1``,``6``) = P(``x_1``,``y_1``)``Q(``5``,``0``) = Q(``x_2``,``y_2``)`Solve using the Midpoint Formula`m` `=` $$(\frac{\color{#7d02aa}{x_1+x_2}}{2},\frac{\color{#00880a}{y_1+y_2}}{2})$$ Midpoint Formula `=` $$(\frac{\color{#7d02aa}{1+5}}{2},\frac{\color{#00880a}{6+0}}{2})$$ Plug in the coordinates `=` `(6/2,6/2)` Simplify `=` `(3,3)` `\text(Midpoint) =(3,3)`
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Question 2 of 7
2. Question
Find the midpoint of the line segment with the given endpoints `A(-3,-2)` and `B(10,-3)`. Give your answer in decimals, if necessary.
- `\text(Midpoint) =` (3.5), (-2.5)
Correct
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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(``-3``,``-2``) = A(``x_1``,``y_1``)``B(``10``,``-3``) = 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 `=` $$(\frac{\color{#9202AA}{-3+10}}{2},\frac{\color{#00880A}{-2+(-3)}}{2})$$ Plug in the coordinates `=` `(7/2,-5/2)` Simplify `=` `(3.5,-2.5)` `\text(Midpoint) =(3.5,-2.5)`
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Question 3 of 7
3. Question
Find the midpoint between the points `A(-4,4)` and `B(2,2)`
- Midpoint`=` (-1), (3)
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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)(4))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(2),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)(-4+2))/(2),(color(forestgreen)(4+2))/(2))` Plug in the coordinates `=` `((-2)/(2),6/2)` Simplify `=` `(-1,3)` Midpoint`=(-1,3)` -
Question 4 of 7
4. Question
Find the midpoint between the points `A(-2,1)` and `B(4,-5)`
- Midpoint`=` (1), (-2)
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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)(-2),color(forestgreen)(1))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(4),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)(-2+4))/(2),(color(forestgreen)(1+(-5)))/(2))` Plug in the coordinates `=` `(2/2,(-4)/2)` Simplify `=` `(1,-2)` Midpoint`=(1,-2)` -
Question 5 of 7
5. Question
Find the midpoint between the points `A(1,4)` and `B(3,0)`
- Midpoint`=` (2), (2)
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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)(4))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(3),color(forestgreen)(0))=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+3))/(2),(color(forestgreen)(4+0))/(2))` Plug in the coordinates `=` `(4/(2),4/2)` Simplify `=` `(2,2)` Midpoint`=(2,2)` -
Question 6 of 7
6. Question
Find the midpoint between the points `A(2,4)` and `B(6,-2)`
- Midpoint`=` (4), (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)(2),color(forestgreen)(4))=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)(2+6))/(2),(color(forestgreen)(4-2))/(2))` Plug in the coordinates `=` `((8)/(2),2/2)` Simplify `=` `(4,1)` Midpoint`=(4,1)` -
Question 7 of 7
7. Question
Find the coordinates of point `T` if `S` is at `(−1,1)` and the midpoint is at `(2,3)`
- `\text(T) =(` (5), (5)`)`
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`S(``-1``,``1``) = S(``x_1``,``y_1``)``m=(2,3)`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 `=` $$(2,3)=(\frac{\color{#9202AA}{-1+x_2}}{2},\frac{\color{#00880A}{1+y_2}}{2})$$ Plug in the coordinates Solve for each coordinate individually$$2$$ `=` $$\frac{\color{#9202AA}{-1+x_2}}{2}$$ $$4$$ `=` $$\color{#9202AA}{-1+x_2}$$ $$\color{#9202AA}{5}$$ `=` $$\color{#9202AA}{x_2}$$ $$\color{#9202AA}{x_2}$$ `=` $$\color{#9202AA}{5}$$ $$3$$ `=` $$\frac{\color{#00880A}{1+y_2}}{2}$$ $$6$$ `=` $$\color{#00880A}{1+y_2}$$ $$\color{#00880A}{5}$$ `=` $$\color{#00880A}{y_2}$$ $$\color{#00880A}{y_2}$$ `=` $$\color{#00880A}{5}$$ Combine obtained values`T=(``x_2``,``y_2``) = T(``5``,``5``)``\text(T) =(5,5)`
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