Math / Geometry

QuestionFind the midpoint of the segment with the given endpoints $(-6,9)$ and $(6,2)$ .
The midpoint of the segment is $\square$ (Simplify your answer. Type an ordered pair.)

Studdy Solution

STEP 1

1. The midpoint of a segment in a 2-dimensional coordinate system can be found using the midpoint formula.
2. The endpoints of the segment are given as $(-6, 9)$ and $(6, 2)$ .

STEP 2

1. Identify the formula for the midpoint of a segment in the coordinate plane.
2. Substitute the given endpoints into the formula.
3. Simplify to find the coordinates of the midpoint.

STEP 3

Identify the formula for the midpoint of a segment in the coordinate plane.
The midpoint formula is:
$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$
where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the endpoints of the segment.

STEP 4

Substitute the given endpoints $(-6, 9)$ and $(6, 2)$ into the midpoint formula.
$\left( \frac{-6 + 6}{2}, \frac{9 + 2}{2} \right)$

STEP 5

Simplify the expression to find the coordinates of the midpoint.
$\left( \frac{0}{2}, \frac{11}{2} \right) = \left( 0, \frac{11}{2} \right)$
The midpoint of the segment is $\left( 0, \frac{11}{2} \right)$ .

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QuestionFind the midpoint of the segment with the given endpoints $(-6,9)$ and $(6,2)$ .
The midpoint of the segment is $\square$ (Simplify your answer. Type an ordered pair.)

Studdy Solution

STEP 1

1. The midpoint of a segment in a 2-dimensional coordinate system can be found using the midpoint formula.
2. The endpoints of the segment are given as $(-6, 9)$ and $(6, 2)$ .

STEP 2

1. Identify the formula for the midpoint of a segment in the coordinate plane.
2. Substitute the given endpoints into the formula.
3. Simplify to find the coordinates of the midpoint.

STEP 3

Identify the formula for the midpoint of a segment in the coordinate plane.
The midpoint formula is:
$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$
where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the endpoints of the segment.

STEP 4

Substitute the given endpoints $(-6, 9)$ and $(6, 2)$ into the midpoint formula.
$\left( \frac{-6 + 6}{2}, \frac{9 + 2}{2} \right)$

STEP 5

Simplify the expression to find the coordinates of the midpoint.
$\left( \frac{0}{2}, \frac{11}{2} \right) = \left( 0, \frac{11}{2} \right)$
The midpoint of the segment is $\left( 0, \frac{11}{2} \right)$ .

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QuestionFind the midpoint of the segment with the given endpoints (−6,9)(-6,9)(−6,9) and (6,2)(6,2)(6,2).The midpoint of the segment is □\square□ (Simplify your answer. Type an ordered pair.)

Studdy Solution

STEP 1

1. The midpoint of a segment in a 2-dimensional coordinate system can be found using the midpoint formula.2. The endpoints of the segment are given as (−6,9)(-6, 9)(−6,9) and (6,2)(6, 2)(6,2).

STEP 2

1. Identify the formula for the midpoint of a segment in the coordinate plane.2. Substitute the given endpoints into the formula.3. Simplify to find the coordinates of the midpoint.

STEP 3

STEP 4

Substitute the given endpoints (−6,9)(-6, 9)(−6,9) and (6,2)(6, 2)(6,2) into the midpoint formula.(−6+62,9+22) \left( \frac{-6 + 6}{2}, \frac{9 + 2}{2} \right) (2−6+6​,29+2​)

STEP 5

Simplify the expression to find the coordinates of the midpoint.(02,112)=(0,112) \left( \frac{0}{2}, \frac{11}{2} \right) = \left( 0, \frac{11}{2} \right) (20​,211​)=(0,211​)The midpoint of the segment is (0,112)\left( 0, \frac{11}{2} \right)(0,211​).

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QuestionFind the midpoint of the segment with the given endpoints $(-6,9)$ and $(6,2)$ .
The midpoint of the segment is $\square$ (Simplify your answer. Type an ordered pair.)

1. The midpoint of a segment in a 2-dimensional coordinate system can be found using the midpoint formula.
2. The endpoints of the segment are given as $(-6, 9)$ and $(6, 2)$ .

1. Identify the formula for the midpoint of a segment in the coordinate plane.
2. Substitute the given endpoints into the formula.
3. Simplify to find the coordinates of the midpoint.

Substitute the given endpoints $(-6, 9)$ and $(6, 2)$ into the midpoint formula.
$\left( \frac{-6 + 6}{2}, \frac{9 + 2}{2} \right)$

Simplify the expression to find the coordinates of the midpoint.
$\left( \frac{0}{2}, \frac{11}{2} \right) = \left( 0, \frac{11}{2} \right)$
The midpoint of the segment is $\left( 0, \frac{11}{2} \right)$ .