Question

The point with coordinates $(6,-10)$ is the midpoint of the segment with one endpoint at $(8,0)$. Find the sum of the coordinates of the other endpoint.

Answer 1

The coordinates of the other endpoint are (4, -20) and the sum of the coordinates is -16.

Step-by-step explanation:

Mathematics: High School

To find the sum of the coordinates of the other endpoint, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points with coordinates (x₁, y₁) and (x₂, y₂) are given by the formula:

x = (x₁ + x₂)/2

y = (y₁ + y₂)/2

In this case, the coordinates of the known midpoint are (6, -10) and one endpoint is (8, 0). By substituting these values into the midpoint formula, we can solve for the coordinates of the other endpoint.

Substituting:

x = (8 + x₂)/2

6 = (8 + x₂)/2

12 = 8 + x₂

4 = x₂

y = (0 + y₂)/2

-10 = (0 + y₂)/2

-20 = 0 + y₂

-20 = y₂

Therefore, the coordinates of the other endpoint are (4, -20). To find the sum of the coordinates, we simply add the x-coordinate and the y-coordinate: 4 + (-20) = -16.

Answer 2

`(4,-20)`

Step-by-step explanation:

Let
`P(x,y),\,Q(u,v)` be two points then midpoint of
`PQ` is given by
`((x+u)/(2),(y+v)/(2))`

Put midpoint as
`(6,-10)` and
`(u,v)=(8,0)`

Therefore,

`((x+u)/(2),(y+v)/(2))=(6,-10)\\\\((x+8)/(2),(y+0)/(2))=(6,-10)\\\\(x+8)/(2)=6,\,(y)/(2)=-10\\\\x+8=12,\,y=-20\\x=12-8,\,y=-20\\x=4,\,y=-20`

So, the other point is
`(4,-20)`