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)

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,

$(4,1)=(\frac{-7+x}{2},\frac{10+y}{2})$

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

Thus, we have,

$4=\frac{7+x}{2}$

$8=7+x$

$15=x$

Thus, the value of x is 15.

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

Thus, we have,

  $1=\frac{10+y}{2}$

  $2=10+y$

$-8=y$

Thus, the value of y is -8

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