Midpoint of a Line 1

Years

Year 9

Coordinate Geometry

Midpoint of a Line

Midpoint of a Line 1

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Question 1 of 7

Find the midpoint of

$PQ$ if

$P(1,6)$ and

$Q(5,0)$

1. $(3,3)$
2. $(2,4)$
3. $(6,6)$
4. $(7/2, 5/2)$

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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

	$=$	$(3,3)$

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

Question 2 of 7

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)

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

$A($ $-3$

$,$ $-2$

$) = A($ $x_1$

$,$ $y_1$

$)$

$B($ $10$

$,$ $-3$

$) = B($ $x_2$

$,$ $y_2$

$)$

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

	$=$	$(3.5,-2.5)$

$\text(Midpoint) =(3.5,-2.5)$

Question 3 of 7

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

Midpoint $=$ (-1), (3)

Question 4 of 7

Find the midpoint between the points $A(-2,1)$ and $B(4,-5)$

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

Question 5 of 7

Find the midpoint between the points $A(1,4)$ and $B(3,0)$

Midpoint $=$ (2), (2)

Question 6 of 7

Find the midpoint between the points $A(2,4)$ and $B(6,-2)$

Midpoint $=$ (4), (1)

Question 7 of 7

Find the coordinates of point

$T$ if

$S$ is at

$(−1,1)$ and the midpoint is at

$(2,3)$

$\text(T) =($ (5), (5) $)$

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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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Quiz summary

Information

1. Question

Hint

Well Done!

Midpoint Formula

2. Question

Excellent!

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

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Midpoint Formula

Quizzes

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