QuestionFind the midpoint of the segment with endpoints $(-2,3)$ and $(5,-3)$ .

Studdy Solution

STEP 1

Assumptions1. The endpoints of the segment are (-,3) and (5,-3). . We are working in a Cartesian coordinate system.

STEP 2

The formula to find the midpoint of a line segment with endpoints $(x1, y1)$ and $(x2, y2)$ in a Cartesian coordinate system is given by $Midpoint = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)$

STEP 3

Now, plug in the given values for the endpoints into the midpoint formula.
$Midpoint = \left(\frac{-2 +5}{2}, \frac{3 + (-3)}{2}\right)$

STEP 4

Calculate the x-coordinate of the midpoint.
$x_{mid} = \frac{-2 +}{2} = \frac{3}{2} =1.$

STEP 5

Calculate the y-coordinate of the midpoint.
$y_{mid} = \frac{3 + (-3)}{2} = \frac{0}{2} =0$

STEP 6

So, the midpoint of the segment with endpoints (-2,3) and (5,-3) is (1.5,0).

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QuestionFind the midpoint of the segment with endpoints $(-2,3)$ and $(5,-3)$ .

Studdy Solution

STEP 1

Assumptions1. The endpoints of the segment are (-,3) and (5,-3). . We are working in a Cartesian coordinate system.

STEP 2

The formula to find the midpoint of a line segment with endpoints $(x1, y1)$ and $(x2, y2)$ in a Cartesian coordinate system is given by $Midpoint = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)$

STEP 3

Now, plug in the given values for the endpoints into the midpoint formula.
$Midpoint = \left(\frac{-2 +5}{2}, \frac{3 + (-3)}{2}\right)$

STEP 4

Calculate the x-coordinate of the midpoint.
$x_{mid} = \frac{-2 +}{2} = \frac{3}{2} =1.$

STEP 5

Calculate the y-coordinate of the midpoint.
$y_{mid} = \frac{3 + (-3)}{2} = \frac{0}{2} =0$

STEP 6

So, the midpoint of the segment with endpoints (-2,3) and (5,-3) is (1.5,0).

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QuestionFind the midpoint of the segment with endpoints (−2,3)(-2,3)(−2,3) and (5,−3)(5,-3)(5,−3).

Studdy Solution

STEP 1

Assumptions1. The endpoints of the segment are (-,3) and (5,-3). . We are working in a Cartesian coordinate system.

STEP 2

The formula to find the midpoint of a line segment with endpoints (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) in a Cartesian coordinate system is given byMidpoint=(x1+x22,y1+y22)Midpoint = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)Midpoint=(2x1+x2​,2y1+y2​)

STEP 3

Now, plug in the given values for the endpoints into the midpoint formula.Midpoint=(−2+52,3+(−3)2)Midpoint = \left(\frac{-2 +5}{2}, \frac{3 + (-3)}{2}\right)Midpoint=(2−2+5​,23+(−3)​)

STEP 4

Calculate the x-coordinate of the midpoint.xmid=−2+2=32=1.x_{mid} = \frac{-2 +}{2} = \frac{3}{2} =1.xmid​=2−2+​=23​=1.

STEP 5

Calculate the y-coordinate of the midpoint.ymid=3+(−3)2=02=0y_{mid} = \frac{3 + (-3)}{2} = \frac{0}{2} =0ymid​=23+(−3)​=20​=0

STEP 6

So, the midpoint of the segment with endpoints (-2,3) and (5,-3) is (1.5,0).

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QuestionFind the midpoint of the segment with endpoints $(-2,3)$ and $(5,-3)$ .

The formula to find the midpoint of a line segment with endpoints $(x1, y1)$ and $(x2, y2)$ in a Cartesian coordinate system is given by $Midpoint = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)$

Now, plug in the given values for the endpoints into the midpoint formula.
$Midpoint = \left(\frac{-2 +5}{2}, \frac{3 + (-3)}{2}\right)$

Calculate the x-coordinate of the midpoint.
$x_{mid} = \frac{-2 +}{2} = \frac{3}{2} =1.$

Calculate the y-coordinate of the midpoint.
$y_{mid} = \frac{3 + (-3)}{2} = \frac{0}{2} =0$