QuestionFind the midpoint of the line segment with endpoints $P(0,9)$ and $Q(10,7)$ . Write coordinates as decimals or integers.

Studdy Solution

STEP 1

Assumptions1. The line segment $\overline{ Q}$ has endpoints at $(0,9)$ and $Q(10,7)$ . . We are looking for the midpoint $M$ of the line segment $\overline{ Q}$ .
3. The coordinates of the midpoint are the averages of the x-coordinates and y-coordinates of the endpoints.

STEP 2

The formula for the midpoint of a line segment with endpoints $(x1, y1)$ and $(x2, y2)$ is $M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)$

STEP 3

Now, plug in the given values for the coordinates of points $$ and $Q$ into the midpoint formula.
$M = \left(\frac{0 +10}{2}, \frac{9 +7}{2}\right)$

STEP 4

Calculate the x-coordinate of the midpoint by averaging the x-coordinates of the endpoints.
$M_x = \frac{0 +10}{2} =$

STEP 5

Calculate the y-coordinate of the midpoint by averaging the y-coordinates of the endpoints.
$M_y = \frac{9 +7}{2} =8$

STEP 6

Now that we have the x-coordinate and y-coordinate of the midpoint, we can write the coordinates of the midpoint $M$ .
$M = (5,8)$ The coordinates of the midpoint $M$ of the line segment $\overline{ Q}$ are $(5,8)$ .

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QuestionFind the midpoint of the line segment with endpoints $P(0,9)$ and $Q(10,7)$ . Write coordinates as decimals or integers.

Studdy Solution

STEP 1

Assumptions1. The line segment $\overline{ Q}$ has endpoints at $(0,9)$ and $Q(10,7)$ . . We are looking for the midpoint $M$ of the line segment $\overline{ Q}$ .
3. The coordinates of the midpoint are the averages of the x-coordinates and y-coordinates of the endpoints.

STEP 2

The formula for the midpoint of a line segment with endpoints $(x1, y1)$ and $(x2, y2)$ is $M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)$

STEP 3

Now, plug in the given values for the coordinates of points $$ and $Q$ into the midpoint formula.
$M = \left(\frac{0 +10}{2}, \frac{9 +7}{2}\right)$

STEP 4

Calculate the x-coordinate of the midpoint by averaging the x-coordinates of the endpoints.
$M_x = \frac{0 +10}{2} =$

STEP 5

Calculate the y-coordinate of the midpoint by averaging the y-coordinates of the endpoints.
$M_y = \frac{9 +7}{2} =8$

STEP 6

Now that we have the x-coordinate and y-coordinate of the midpoint, we can write the coordinates of the midpoint $M$ .
$M = (5,8)$ The coordinates of the midpoint $M$ of the line segment $\overline{ Q}$ are $(5,8)$ .

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QuestionFind the midpoint of the line segment with endpoints P(0,9)P(0,9)P(0,9) and Q(10,7)Q(10,7)Q(10,7). Write coordinates as decimals or integers.

Studdy Solution

STEP 1

STEP 2

The formula for the midpoint of a line segment with endpoints (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) isM=(x1+x22,y1+y22)M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)M=(2x1+x2​,2y1+y2​)

STEP 3

Now, plug in the given values for the coordinates of points $$ and $Q$ into the midpoint formula.M=(0+102,9+72)M = \left(\frac{0 +10}{2}, \frac{9 +7}{2}\right)M=(20+10​,29+7​)

STEP 4

Calculate the x-coordinate of the midpoint by averaging the x-coordinates of the endpoints.Mx=0+102=M_x = \frac{0 +10}{2} =Mx​=20+10​=

STEP 5

Calculate the y-coordinate of the midpoint by averaging the y-coordinates of the endpoints.My=9+72=8M_y = \frac{9 +7}{2} =8My​=29+7​=8

STEP 6

Now that we have the x-coordinate and y-coordinate of the midpoint, we can write the coordinates of the midpoint MMM.M=(5,8)M = (5,8)M=(5,8)The coordinates of the midpoint MMM of the line segment Q‾\overline{ Q}Q​ are (5,8)(5,8)(5,8).

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QuestionFind the midpoint of the line segment with endpoints $P(0,9)$ and $Q(10,7)$ . Write coordinates as decimals or integers.

The formula for the midpoint of a line segment with endpoints $(x1, y1)$ and $(x2, y2)$ is $M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)$

Now, plug in the given values for the coordinates of points $$ and $Q$ into the midpoint formula.
$M = \left(\frac{0 +10}{2}, \frac{9 +7}{2}\right)$

Calculate the x-coordinate of the midpoint by averaging the x-coordinates of the endpoints.
$M_x = \frac{0 +10}{2} =$

Calculate the y-coordinate of the midpoint by averaging the y-coordinates of the endpoints.
$M_y = \frac{9 +7}{2} =8$

Now that we have the x-coordinate and y-coordinate of the midpoint, we can write the coordinates of the midpoint $M$ .
$M = (5,8)$ The coordinates of the midpoint $M$ of the line segment $\overline{ Q}$ are $(5,8)$ .