Midpoint of a Line 3
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Question 1 of 6
1. Question
Find the midpoint between the points `A(-4,5)` and `B(7,4)`
- Midpoint`=` (1.5), (4.5)
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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)(5))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(7),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+7))/(2),(color(forestgreen)(5+4))/(2))` Plug in the coordinates `=` `((3)/(2),9/2)` Simplify `=` `(1.5,4.5)` Midpoint`=(1.5,4.5)` -
Question 2 of 6
2. Question
Find the midpoint between the points `A(3,5)` and `B(-3,-3)`
- Midpoint`=` (0), (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)(3),color(forestgreen)(5))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(-3),color(forestgreen)(-3))=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)(3-3))/(2),(color(forestgreen)(5-3))/(2))` Plug in the coordinates `=` `((0)/(2),2/2)` Simplify `=` `(0,1)` Midpoint`=(0,1)` -
Question 3 of 6
3. Question
Find the midpoint between the points `A(4,1)` and `B(1,-10)`
- Midpoint`=` (2.5), (-4.5)
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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)(1))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(1),color(forestgreen)(-10))=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+1))/(2),(color(forestgreen)(1-10))/(2))` Plug in the coordinates `=` `((5)/(2),(-9)/2)` Simplify `=` `(2.5,-4.5)` Midpoint`=(2.5,-4.5)` -
Question 4 of 6
4. Question
Find the midpoint between the points `A(-1,-6)` and `B(3,2)`
- 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)(-1),color(forestgreen)(-6))=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)(-1+3))/(2),(color(forestgreen)(-6+2))/(2))` Plug in the coordinates `=` `((2)/(2),(-4)/2)` Simplify `=` `(1,-2)` Midpoint`=(1,-2)` -
Question 5 of 6
5. Question
Find the midpoint between the points `A(-6,3)` and `B(-2,-5)`
- 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)(-6),color(forestgreen)(3))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))``B(color(darkviolet)(-2),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)(-6-2))/(2),(color(forestgreen)(3-5))/(2))` Plug in the coordinates `=` `((-8)/(2),(-2)/2)` Simplify `=` `(-4,-1)` Midpoint`=(-4,-1)` -
Question 6 of 6
6. Question
Given the midpoint `M(-3,-9)` and one endpoint `A(-1,-3)` of a line segment, find the other endpoint `B \text((Unknown))`
- `\text(B) =(` (-5), (-15)`)`
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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``,``-3``) = A(``x_1``,``y_1``)``m=(-3,-9)`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 `=` $$(-3,-9)=(\frac{\color{#9202AA}{-1+x_2}}{2},\frac{\color{#00880A}{-3+y_2}}{2})$$ Plug in the coordinates Solve for each coordinate individually$$-3$$ `=` $$\frac{\color{#9202AA}{-1+x_2}}{2}$$ $$-6$$ `=` $$\color{#9202AA}{-1+x_2}$$ $$\color{#9202AA}{-5}$$ `=` $$\color{#9202AA}{x_2}$$ $$\color{#9202AA}{x_2}$$ `=` $$\color{#9202AA}{-5}$$ $$-9$$ `=` $$\frac{\color{#00880A}{-3+y_2}}{2}$$ $$-18$$ `=` $$\color{#00880A}{-3+y_2}$$ $$\color{#00880A}{-15}$$ `=` $$\color{#00880A}{y_2}$$ $$\color{#00880A}{y_2}$$ `=` $$\color{#00880A}{-15}$$ Combine obtained values`B=(``x_2``,``y_2``) = B(``-5``,``-15``)``\text(B) =(-5,-15)`
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- Midpoint of a Line 3
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- Gradient Intercept Form: Graph an Equation 1
- Gradient Intercept Form: Graph an Equation 2
- Gradient Intercept Form: Write an Equation 1
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- Graph Linear Inequalities 1
- Graph Linear Inequalities 2
- Convert Between General Form and Gradient Intercept Form 1
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- Perpendicular Lines 1
- Perpendicular Lines 2