Math / Geometry

QuestionFind the midpoint of the line segment joining the points $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ . $P_{1}=(3,-3) ; P_{2}=(5,3)$
The midpoint of the line segment joining the points $P_{1}$ and $P_{2}$ is $\square$ . (Simplify your answer. Type an ordered pair.)

Studdy Solution

STEP 1

What is this asking? Find the middle point between two given points on a graph! Watch out! Don't mix up the $x$ and $y$ coordinates!
Also, remember the midpoint formula is about averages!

STEP 2

1. Find the $x$ -coordinate of the midpoint.
2. Find the $y$ -coordinate of the midpoint.
3. Combine the coordinates.

STEP 3

The $x$ -coordinate of the midpoint is the average of the $x$ -coordinates of the two endpoints.
Think of it like this: if you're meeting a friend halfway between your houses, you both travel the same distance.
Finding the average $x$ -coordinate is like finding that halfway point!

STEP 4

Our two $x$ -coordinates are $x_1 = 3$ and $x_2 = 5$ .
Let's add them together and divide by $\textbf{2}$ to find the average: $\frac{x_1 + x_2}{2} = \frac{3 + 5}{2} = \frac{8}{2} = \textbf{4}$ So, the $x$ -coordinate of our midpoint is 4!

STEP 5

Just like with the $x$ -coordinate, the $y$ -coordinate of the midpoint is the average of the $y$ -coordinates of the two endpoints.

STEP 6

Our two $y$ -coordinates are $y_1 = -3$ and $y_2 = 3$ .
Let's add them together and divide by $\textbf{2}$ to find the average: $\frac{y_1 + y_2}{2} = \frac{-3 + 3}{2} = \frac{0}{2} = \textbf{0}$ The $y$ -coordinate of our midpoint is 0!

STEP 7

Now, let's put the $x$ and $y$ coordinates together to get our midpoint!
We found that the $x$ -coordinate is 4 and the $y$ -coordinate is 0.

STEP 8

The midpoint is written as an ordered pair $(x, y)$ , so our midpoint is $\textbf{(4, 0)}$ !
Boom!

STEP 9

The midpoint of the line segment joining the points $(3, -3)$ and $(5, 3)$ is $(4, 0)$ .

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QuestionFind the midpoint of the line segment joining the points $\mathrm{P}_{1}$ and $\mathrm{P}_{2}$ . $P_{1}=(3,-3) ; P_{2}=(5,3)$
The midpoint of the line segment joining the points $P_{1}$ and $P_{2}$ is $\square$ . (Simplify your answer. Type an ordered pair.)

Studdy Solution

STEP 1

What is this asking? Find the middle point between two given points on a graph! Watch out! Don't mix up the $x$ and $y$ coordinates!
Also, remember the midpoint formula is about averages!

STEP 2

1. Find the $x$ -coordinate of the midpoint.
2. Find the $y$ -coordinate of the midpoint.
3. Combine the coordinates.

STEP 3

The $x$ -coordinate of the midpoint is the average of the $x$ -coordinates of the two endpoints.
Think of it like this: if you're meeting a friend halfway between your houses, you both travel the same distance.
Finding the average $x$ -coordinate is like finding that halfway point!

STEP 4

Our two $x$ -coordinates are $x_1 = 3$ and $x_2 = 5$ .
Let's add them together and divide by $\textbf{2}$ to find the average: $\frac{x_1 + x_2}{2} = \frac{3 + 5}{2} = \frac{8}{2} = \textbf{4}$ So, the $x$ -coordinate of our midpoint is 4!

STEP 5

Just like with the $x$ -coordinate, the $y$ -coordinate of the midpoint is the average of the $y$ -coordinates of the two endpoints.

STEP 6

Our two $y$ -coordinates are $y_1 = -3$ and $y_2 = 3$ .
Let's add them together and divide by $\textbf{2}$ to find the average: $\frac{y_1 + y_2}{2} = \frac{-3 + 3}{2} = \frac{0}{2} = \textbf{0}$ The $y$ -coordinate of our midpoint is 0!

STEP 7

Now, let's put the $x$ and $y$ coordinates together to get our midpoint!
We found that the $x$ -coordinate is 4 and the $y$ -coordinate is 0.

STEP 8

The midpoint is written as an ordered pair $(x, y)$ , so our midpoint is $\textbf{(4, 0)}$ !
Boom!

STEP 9

The midpoint of the line segment joining the points $(3, -3)$ and $(5, 3)$ is $(4, 0)$ .

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Studdy Solution

STEP 1

What is this asking? Find the middle point between two given points on a graph! Watch out! Don't mix up the xxx and yyy coordinates!Also, remember the midpoint formula is about *averages*!

STEP 2

1. Find the xxx-coordinate of the midpoint.2. Find the yyy-coordinate of the midpoint.3. Combine the coordinates.

STEP 3

The xxx-coordinate of the midpoint is the average of the xxx-coordinates of the two endpoints.Think of it like this: if you're meeting a friend halfway between your houses, you both travel the same distance.Finding the average xxx-coordinate is like finding that halfway point!

STEP 4

STEP 5

Just like with the xxx-coordinate, the yyy-coordinate of the midpoint is the average of the yyy-coordinates of the two endpoints.

STEP 6

STEP 7

Now, let's put the xxx and yyy coordinates together to get our midpoint!We found that the xxx-coordinate is **4** and the yyy-coordinate is **0**.

STEP 8

The midpoint is written as an ordered pair (x,y)(x, y)(x,y), so our midpoint is (4, 0)\textbf{(4, 0)}(4, 0)!Boom!

STEP 9

The midpoint of the line segment joining the points (3,−3)(3, -3)(3,−3) and (5,3)(5, 3)(5,3) is (4,0)(4, 0)(4,0).

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Find the middle point between two given points on a graph! Watch out! Don't mix up the $x$ and $y$ coordinates!
Also, remember the midpoint formula is about averages!

1. Find the $x$ -coordinate of the midpoint.
2. Find the $y$ -coordinate of the midpoint.
3. Combine the coordinates.

The $x$ -coordinate of the midpoint is the average of the $x$ -coordinates of the two endpoints.
Think of it like this: if you're meeting a friend halfway between your houses, you both travel the same distance.
Finding the average $x$ -coordinate is like finding that halfway point!

Just like with the $x$ -coordinate, the $y$ -coordinate of the midpoint is the average of the $y$ -coordinates of the two endpoints.

Now, let's put the $x$ and $y$ coordinates together to get our midpoint!
We found that the $x$ -coordinate is 4 and the $y$ -coordinate is 0.

The midpoint is written as an ordered pair $(x, y)$ , so our midpoint is $\textbf{(4, 0)}$ !
Boom!

The midpoint of the line segment joining the points $(3, -3)$ and $(5, 3)$ is $(4, 0)$ .