Question

Given the midpoint and one endpoint of a line segment, find the other endpoint.

Endpoint (-7,10), midpoint (4,1)

Answer 1

The other endpoint is (15,-8)

Step-by-step explanation:

Given that the midpoint is (4,1) and the endpoint is (-7,10)

We need to determine the other endpoint.

Endpoint:

Let (x,y) denote the other endpoint.

We shall determine the other endpoint using the midpoint formula.

Hence, substituting the values in the midpoint formula, we have,

`(4,1)=((-7+x)/(2),(10+y)/(2))`

Let us equate the x - coordinates to determine the value of x.

Thus, we have,

`4=(7+x)/(2)`

`8=7+x`

`15=x`

Thus, the value of x is 15.

Similarly, let us equate the y - coordinate to determine the value of y.

Thus, we have,

`1=(10+y)/(2)`

`2=10+y`

`-8=y`

Thus, the value of y is -8

Therefore, the other endpoint is (15,-8)