Midpoint of a Line 3

Topics

Algebra 2

Linear Equations and Graphs

Midpoint of a Line

Midpoint of a Line 3

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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)

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)

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)

Question 4 of 6

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

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

Question 5 of 6

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

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

Question 6 of 6

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) $)$

Incorrect

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

$B=($ $x_2$

$,$ $y_2$

$) = B($ $-5$

$,$ $-15$

$)$

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

Midpoint of a Line 3

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Quiz summary

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1. Question

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Midpoint Formula

2. Question

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Midpoint Formula

3. Question

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Midpoint Formula

4. Question

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Midpoint Formula

5. Question

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Midpoint Formula

6. Question

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Midpoint Formula

Quizzes

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