Math  /  Geometry

QuestionC(15,3)C(15,3) and D(6,15)D(6,15) are the endpoints of a line segment. What is the midpoint MM of that line segment? ( 3{ }^{3}. 7 , Write the coordinates as decimals or integers. M=(,)M=(\square, \square) Sulinit

Studdy Solution

STEP 1

What is this asking? Find the middle point of a line connecting two points on a graph. Watch out! Don't mix up the xx and yy coordinates!

STEP 2

1. Find the Midpoint's xx-coordinate
2. Find the Midpoint's yy-coordinate
3. Combine into the Midpoint

STEP 3

The xx-coordinate of point CC is 1515, and the xx-coordinate of point DD is 66.
To find the midpoint's xx-coordinate, we **average** these two values.
It's like finding a halfway point on a number line!

STEP 4

xM=xC+xD2x_M = \frac{x_C + x_D}{2} This formula takes the **sum** of the xx-coordinates of CC and DD and **divides** by 22 to find the average.

STEP 5

**Substitute** the given values: xM=15+62x_M = \frac{15 + 6}{2}

STEP 6

**Calculate** the sum: xM=212x_M = \frac{21}{2}

STEP 7

**Divide** to get the midpoint's xx-coordinate: xM=10.5x_M = 10.5

STEP 8

Now, let's do the same thing for the yy-coordinates!
The yy-coordinate of point CC is 33, and the yy-coordinate of point DD is 1515.

STEP 9

We use the same midpoint formula, but this time with the yy-coordinates: yM=yC+yD2y_M = \frac{y_C + y_D}{2}

STEP 10

**Substitute** the given yy values: yM=3+152y_M = \frac{3 + 15}{2}

STEP 11

**Calculate** the sum: yM=182y_M = \frac{18}{2}

STEP 12

**Divide** to get the midpoint's yy-coordinate: yM=9y_M = 9

STEP 13

We found that the midpoint's xx-coordinate is 10.510.5 and the yy-coordinate is 99.
So, the **midpoint** MM is (10.5,9)(10.5, 9).
Awesome!

STEP 14

M=(10.5,9)M = (10.5, 9)

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