Midpoint of a Line 3

Question 1 of 6

Find the midpoint between the points $A (- 4, 5)$ $A(-4,5)$ and $B (7, 4)$ $B(7,4)$

Midpoint $=$ $=$ (1.5), (4.5)

Incorrect

Midpoint Formula

M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

$M=((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))$

First, label the given coordinates

A (- 4, 5) = A (x_{1}, y_{1})

$A(color(darkviolet)(-4),color(forestgreen)(5))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

B (7, 4) = B (x_{2}, y_{2})

$B(color(darkviolet)(7),color(forestgreen)(4))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

Solve using the Midpoint Formula

Midpoint	$=$ $=$	$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))$	Midpoint Formula
	$=$ $=$	$(\frac{- 4 + 7}{2}, \frac{5 + 4}{2})$ $((color(darkviolet)(-4+7))/(2),(color(forestgreen)(5+4))/(2))$	Plug in the coordinates
	$=$ $=$	$(\frac{3}{2}, \frac{9}{2})$ $((3)/(2),9/2)$	Simplify
	$=$ $=$	$(1.5, 4.5)$ $(1.5,4.5)$

Midpoint

= (1.5, 4.5)

$=(1.5,4.5)$

Question 2 of 6

Find the midpoint between the points $A (3, 5)$ $A(3,5)$ and $B (- 3, - 3)$ $B(-3,-3)$

Midpoint $=$ $=$ (0), (1)

Incorrect

Midpoint Formula

M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

$M=((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))$

First, label the given coordinates

A (3, 5) = A (x_{1}, y_{1})

$A(color(darkviolet)(3),color(forestgreen)(5))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

B (- 3, - 3) = B (x_{2}, y_{2})

$B(color(darkviolet)(-3),color(forestgreen)(-3))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

Solve using the Midpoint Formula

Midpoint	$=$ $=$	$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))$	Midpoint Formula
	$=$ $=$	$(\frac{3 - 3}{2}, \frac{5 - 3}{2})$ $((color(darkviolet)(3-3))/(2),(color(forestgreen)(5-3))/(2))$	Plug in the coordinates
	$=$ $=$	$(\frac{0}{2}, \frac{2}{2})$ $((0)/(2),2/2)$	Simplify
	$=$ $=$	$(0, 1)$ $(0,1)$

Midpoint

= (0, 1)

$=(0,1)$

Question 3 of 6

Find the midpoint between the points $A (4, 1)$ $A(4,1)$ and $B (1, - 10)$ $B(1,-10)$

Midpoint $=$ $=$ (2.5), (-4.5)

Incorrect

Midpoint Formula

M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

$M=((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))$

First, label the given coordinates

A (4, 1) = A (x_{1}, y_{1})

$A(color(darkviolet)(4),color(forestgreen)(1))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

B (1, - 10) = B (x_{2}, y_{2})

$B(color(darkviolet)(1),color(forestgreen)(-10))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

Solve using the Midpoint Formula

Midpoint	$=$ $=$	$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))$	Midpoint Formula
	$=$ $=$	$(\frac{4 + 1}{2}, \frac{1 - 10}{2})$ $((color(darkviolet)(4+1))/(2),(color(forestgreen)(1-10))/(2))$	Plug in the coordinates
	$=$ $=$	$(\frac{5}{2}, \frac{- 9}{2})$ $((5)/(2),(-9)/2)$	Simplify
	$=$ $=$	$(2.5, - 4.5)$ $(2.5,-4.5)$

Midpoint

= (2.5, - 4.5)

$=(2.5,-4.5)$

Question 4 of 6

Find the midpoint between the points $A (- 1, - 6)$ $A(-1,-6)$ and $B (3, 2)$ $B(3,2)$

Midpoint $=$ $=$ (1), (-2)

Incorrect

Midpoint Formula

M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

$M=((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))$

First, label the given coordinates

A (- 1, - 6) = A (x_{1}, y_{1})

$A(color(darkviolet)(-1),color(forestgreen)(-6))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

B (3, 2) = B (x_{2}, y_{2})

$B(color(darkviolet)(3),color(forestgreen)(2))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

Solve using the Midpoint Formula

Midpoint	$=$ $=$	$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))$	Midpoint Formula
	$=$ $=$	$(\frac{- 1 + 3}{2}, \frac{- 6 + 2}{2})$ $((color(darkviolet)(-1+3))/(2),(color(forestgreen)(-6+2))/(2))$	Plug in the coordinates
	$=$ $=$	$(\frac{2}{2}, \frac{- 4}{2})$ $((2)/(2),(-4)/2)$	Simplify
	$=$ $=$	$(1, - 2)$ $(1,-2)$

Midpoint

= (1, - 2)

$=(1,-2)$

Question 5 of 6

Find the midpoint between the points $A (- 6, 3)$ $A(-6,3)$ and $B (- 2, - 5)$ $B(-2,-5)$

Midpoint $=$ $=$ (-4), (-1)

Incorrect

Midpoint Formula

M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

$M=((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))$

First, label the given coordinates

A (- 6, 3) = A (x_{1}, y_{1})

$A(color(darkviolet)(-6),color(forestgreen)(3))=A(color(darkviolet)(x_1),color(forestgreen)(y_1))$

B (- 2, - 5) = B (x_{2}, y_{2})

$B(color(darkviolet)(-2),color(forestgreen)(-5))=B(color(darkviolet)(x_2),color(forestgreen)(y_2))$

Solve using the Midpoint Formula

Midpoint	$=$ $=$	$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $((color(darkviolet)(x_1+x_2))/(2),(color(forestgreen)(y_1+y_2))/(2))$	Midpoint Formula
	$=$ $=$	$(\frac{- 6 - 2}{2}, \frac{3 - 5}{2})$ $((color(darkviolet)(-6-2))/(2),(color(forestgreen)(3-5))/(2))$	Plug in the coordinates
	$=$ $=$	$(\frac{- 8}{2}, \frac{- 2}{2})$ $((-8)/(2),(-2)/2)$	Simplify
	$=$ $=$	$(- 4, - 1)$ $(-4,-1)$

Midpoint

= (- 4, - 1)

$=(-4,-1)$

Question 6 of 6

Given the midpoint

M (- 3, - 9)

$M(-3,-9)$ and one endpoint

A (- 1, - 3)

$A(-1,-3)$ of a line segment, find the other endpoint

B (Unknown)

$B \text((Unknown))$

$B = ($ $\text(B) =($ (-5), (-15) $)$ $)$

Incorrect

Midpoint Formula

Midpoint = m = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

$\text{Midpoint}=m=(\frac{\color{#9202AA}{x_1+x_2}}{2},\frac{\color{#00880A}{y_1+y_2}}{2})$

First, label the given coordinates

A (

$A($ $- 1$ $-1$

,

$,$ $- 3$ $-3$

) = A (

$) = A($ $x_{1}$ $x_1$

,

$,$ $y_{1}$ $y_1$

)

$)$

m = (- 3, - 9)

$m=(-3,-9)$

Substitute the values into the Midpoint Formula

$m$ $m$	$=$ $=$	$(\frac{\color{#9202AA}{x_1+x_2}}{2},\frac{\color{#00880A}{y_1+y_2}}{2})$	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 = (

$B=($ $x_{2}$ $x_2$

,

$,$ $y_{2}$ $y_2$

) = B (

$) = B($ $- 5$ $-5$

,

$,$ $- 15$ $-15$

)

$)$

B = (- 5, - 15)

$\text(B) =(-5,-15)$

Midpoint of a Line 3

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Midpoint Formula

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