Midpoint of a Line 2

Topics

Algebra 1

Linear Equations and Graphs

Midpoint of a Line

Midpoint of a Line 2

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Question 1 of 7

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)

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

$A($ $7$

$,$ $3$

$) = A($ $x_1$

$,$ $y_1$

$)$

$B($ $-5$

$,$ $10$

$) = B($ $x_2$

$,$ $y_2$

$)$

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

	$=$	$(1,6.5)$

$\text(Midpoint) =(1,6.5)$

Question 2 of 7

Find the coordinates of point

$M$ if

$A$ is at

$(1,2)$ and

$B$ is at

$(5,6)$

$\text(M) =($ (3), (4) $)$

Incorrect

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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

	$=$	$(3,4)$

$\text(Midpoint) =(3,4)$

Question 3 of 7

Find the midpoint between the points $A(-4,-2)$ and $B(2,4)$

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

Question 4 of 7

Find the midpoint between the points $A(-1,3)$ and $B(8,-5)$

Midpoint $=$ (3.5), (-1)

Question 5 of 7

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

Midpoint $=$ (4.5), (0)

Question 6 of 7

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

Midpoint $=$ (4.5), (0)

Question 7 of 7

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) $)$

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

$A($ $-10$

$,$ $-2$

$) = A($ $x_1$

$,$ $y_1$

$)$

$m=(4,4)$

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

$B=($ $x_2$

$,$ $y_2$

$) = B($ $18$

$,$ $10$

$)$

$\text(B) =(18,10)$

Midpoint of a Line 2

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Quiz summary

Information

1. Question

Nice Job!

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

7. Question

Correct!

Midpoint Formula

Quizzes

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