QuestionFind the coordinates of the endpoint of $\overline{X Y}$ if one endpoint is $(8,-10)$ and the midpoint is at the origin.

Studdy Solution

STEP 1

Assumptions1. The midpoint of the line segment $\overline{X Y}$ is at the origin, which has coordinates (0,0). . One endpoint of the line segment $\overline{X Y}$ has coordinates (8,-10).
3. We need to find the coordinates of the other endpoint of the line segment $\overline{X Y}$ .

STEP 2

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

STEP 3

We know that the midpoint is at the origin (0,0), and one of the endpoints is (8,-10). We can set up the following equations to solve for the coordinates of the other endpoint $(x2, y2)$ $\frac{x1+x2}{2} =0$ $\frac{y1+y2}{2} =0$

STEP 4

Substitute the known values into the equations $\frac{8+x2}{2} =0$ $\frac{-10+y2}{2} =0$

STEP 5

olve the equations for $x2$ and $y2$ $x2 = -8$ $y2 =10$ So, the coordinates of the other endpoint of $\overline{X Y}$ are $(-8,10)$ .

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QuestionFind the coordinates of the endpoint of $\overline{X Y}$ if one endpoint is $(8,-10)$ and the midpoint is at the origin.

Studdy Solution

STEP 1

Assumptions1. The midpoint of the line segment $\overline{X Y}$ is at the origin, which has coordinates (0,0). . One endpoint of the line segment $\overline{X Y}$ has coordinates (8,-10).
3. We need to find the coordinates of the other endpoint of the line segment $\overline{X Y}$ .

STEP 2

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

STEP 3

We know that the midpoint is at the origin (0,0), and one of the endpoints is (8,-10). We can set up the following equations to solve for the coordinates of the other endpoint $(x2, y2)$ $\frac{x1+x2}{2} =0$ $\frac{y1+y2}{2} =0$

STEP 4

Substitute the known values into the equations $\frac{8+x2}{2} =0$ $\frac{-10+y2}{2} =0$

STEP 5

olve the equations for $x2$ and $y2$ $x2 = -8$ $y2 =10$ So, the coordinates of the other endpoint of $\overline{X Y}$ are $(-8,10)$ .

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QuestionFind the coordinates of the endpoint of XY‾\overline{X Y}XY if one endpoint is (8,−10)(8,-10)(8,−10) and the midpoint is at the origin.

Studdy Solution

STEP 1

Assumptions1. The midpoint of the line segment XY‾\overline{X Y}XY is at the origin, which has coordinates (0,0). . One endpoint of the line segment XY‾\overline{X Y}XY has coordinates (8,-10).3. We need to find the coordinates of the other endpoint of the line segment XY‾\overline{X Y}XY.

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) 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

We know that the midpoint is at the origin (0,0), and one of the endpoints is (8,-10). We can set up the following equations to solve for the coordinates of the other endpoint (x2,y2)(x2, y2)(x2,y2)x1+x22=0\frac{x1+x2}{2} =02x1+x2​=0y1+y22=0\frac{y1+y2}{2} =02y1+y2​=0

STEP 4

Substitute the known values into the equations8+x22=0\frac{8+x2}{2} =028+x2​=0−10+y22=0\frac{-10+y2}{2} =02−10+y2​=0

STEP 5

olve the equations for x2x2x2 and y2y2y2x2=−8x2 = -8x2=−8y2=10y2 =10y2=10So, the coordinates of the other endpoint of XY‾\overline{X Y}XY are (−8,10)(-8,10)(−8,10).

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QuestionFind the coordinates of the endpoint of $\overline{X Y}$ if one endpoint is $(8,-10)$ and the midpoint is at the origin.

Assumptions1. The midpoint of the line segment $\overline{X Y}$ is at the origin, which has coordinates (0,0). . One endpoint of the line segment $\overline{X Y}$ has coordinates (8,-10).
3. We need to find the coordinates of the other endpoint of the line segment $\overline{X Y}$ .

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

We know that the midpoint is at the origin (0,0), and one of the endpoints is (8,-10). We can set up the following equations to solve for the coordinates of the other endpoint $(x2, y2)$ $\frac{x1+x2}{2} =0$ $\frac{y1+y2}{2} =0$

Substitute the known values into the equations $\frac{8+x2}{2} =0$ $\frac{-10+y2}{2} =0$

olve the equations for $x2$ and $y2$ $x2 = -8$ $y2 =10$ So, the coordinates of the other endpoint of $\overline{X Y}$ are $(-8,10)$ .