Question

One endpoint of a line segment has coordinates represented by (x+2,14y). The midpoint of the line segment is (6,−3).How are the coordinates of the other endpoint expressed in terms of x and y?

Answer 1

To find the coordinates of the other endpoint of a line segment when one endpoint and the midpoint are known, we use the midpoint formula to set up equations and solve for the unknown endpoint, resulting in coordinates (10 - x, -6 - 14y).

Step-by-step explanation:

To find the coordinates of the other endpoint of a line segment where we know one endpoint and the midpoint, we use the midpoint formula. The midpoint formula is expressed as M = ((x1 + x2)/2, (y1 + y2)/2), where M is the midpoint and (x1, y1) and (x2, y2) are the endpoints. Since we know the midpoint is (6, -3) and one endpoint is (x+2, 14y), we set up equations to solve for the other endpoint:

• For the x-coordinate: (x + x2)/2 = 6 → x2 = 2*6 - x - 2
• For the y-coordinate: (14y + y2)/2 = -3 → y2 = 2*(-3) - 14y

Now, we simplify the equations to find the other endpoint:

• x2 = 12 - x - 2 → x2 = 10 - x
• y2 = -6 - 14y → y2 = -6 - 14y

Therefore, the coordinates of the other endpoint are expressed as (10 - x, -6 - 14y).

Answer 2

We are given that one of the endpoints of the line segment is: (x + 2, 14 y)

And that the midpoint of the line segment is: (6,−3)

We can consider using the midpoint formula:

`M=(x_1+x_2)/(2),(y_1+y_2)/(2)`

Substituting:

`\begin{gathered} 6=((x+2)+x_2)/(2) \\ \\ -3=(14y+y_2)/(2) \end{gathered}`

Solving for x₂ and y₂:

`\begin{gathered} 12=x+2+x_2 \\ x_2=10-x \\ \\ -6=14y+y_2 \\ y_2=-14y-6 \end{gathered}`

ANSWER

the other coordinate expressed in terms of x and y is: (10 - x, - 14y - 6)