Question

Find the other endpoint of the line segment with the given endpoint and midpoint

Answer 1

Answer:

The other endpoint is (11,-9)

Step-by-step explanation:

Midpoint Formula

$\large\boxed{(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )}$

We already know the another endpoint which is (3,5). We substitute x = 3 and y = 5 in the formula. You can substitute in x1, x2 or y1, y2. I'll substitute in first x-term and first y-term instead.

$\large{\begin{cases} \frac{3+x}{2}=7\\\frac{5+y}{2}=-2 \end{cases}}$

Because sum of two x-coordinate (along with y-coordinate) divided by two must equal to the midpoint (Let's say that you get the value of midpoint when using midpoint formula.)

Solve the equation for both terms.

$\large{\begin{cases} \frac{3+x}{2}=7\\\frac{5+y}{2}=-2 \end{cases}}$

Cancel the denominator by multiplying the whole equation by 2.

$\large{\begin{cases} \frac{3+x}{2}(2)=7(2)\\\frac{5+y}{2}(2)=-2(2) \end{cases}}\\\large{\begin{cases} 3+x=14\\ 5+y=-4 \end{cases}}$

Isolate x-term and y-term.

$\end{cases}}\\\large{\begin{cases} 3+x=14\\ 5+y=-4 \end{cases}}\\\end{cases}}\\\large{\begin{cases} x=14-3\\ y=-4-5 \end{cases}}\\\end{cases}}\\\large{\begin{cases} x=11\\ y=-9 \end{cases}}$

Therefore, when x = 11, y = -9. We can write in ordered pair as (11,-9). The ordered pair (11,-9) is our other endpoint of the line segment. This can be proved by using the distance formula between midpoint and endpoints.

Note: The distance of (3,5) and (7,-2) must equal to the distance of (11,-9) and (7,-2)