Question

. A segment has a midpoint at (2, -7) and an endpoint at (8, -5). What are the coordinates of the other endpoint?

Answer 1

Ok, you can refer to the midpoint formula to find the endpoint.  Here goes...


MP=(2,-7) and EP=(8,-5)
Let x represent the missing endpoint.
(8+x)/2=2      NOTE: =2 represents first number of MP and the representation of number 8 is self explanatory.  You have two endpoints but need to identify the other endpoint so you divide by 2.  Then, multiply by two on both sides.
2(8+x)/2 = 2*2
16+x/2=4 do the next step (simplify) on the left side of equation 16x/2=8
Now, subtract 4-8=-4  So, the x coordinated of the missing endpoint is -4.

Answer 2

Answer : The coordinates of another endpoint is, (-4, -9)

Step-by-step explanation :

The expression used to calculate the coordinates of another endpoint of a segment with midpoint is:

Let the coordinates of midpoint be, (x,y)

The coordinates of one endpoint be, (x₁,y₁)

The coordinates of another endpoint be, (x₂,y₂)

$(x,y)=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}$

As we are given that:

(x,y) = (2, -7)

(x₁,y₁) = (8, -5)

Now put all the given values in the above expression, we get:

$(x,y)=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}$

$x=\frac{x_1+x_2}{2}$ and $y=\frac{y_1+y_2}{2}$

$2=\frac{8+x_2}{2}$ and $-7=\frac{-5+y_2}{2}$

$x_2=-4$ and $y_2=-9$

Thus, the coordinates of another endpoint is, (x₂,y₂) = (-4, -9)