Question

The midpoint of BC is (5, -2). One endpoint is B (3,4). What are the coordinates of endpoint C?

Answer 1

Let the midpoint of $BC$ be $M(x_{_M};~y_{_M})$.

Then $x_{_M}=\dfrac{x_{_B}+x_{_C}}{2}$ and $y_{_M}=\dfrac{y_{_B}+y_{_C}}{2}$.

We are given $x_{_M}=5, y_{_M}=-2$ and $x_{_B}=3, y_{_B}=4$.

$5=\dfrac{3+x_{_C}}{2}\Rightarrow x_{_C}=7\medskip\\{-2}=\dfrac{4+y_{_C}}{2}\Rightarrow y_{_C}=-8$

$C(7;-8)$

Answer 2

Answer:

The coordinates of endpoint C are (7,-8).

Step-by-step explanation:

Given information: Midpoint of BC is (5, -2) and B(3,4).

We need to find the coordinates of C.

Let the coordinate of C are (x,y).

If end points of a line segment are $(x_1,y_1)$ and $(x_2,y_2)$, then the midpoint of that segment is

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

Midpoint of BC is

$Midpoint=(\frac{3+x}{2},\frac{4+y}{2})$

Midpoint of BC is (5,-2).

$(5,-2)=(\frac{3+x}{2},\frac{4+y}{2})$

On comparing both sides.

$5=\frac{3+x}{2}$

$10=3+x$

$10-3=x$

$7=x$

The value of x is 7.

$-2=\frac{4+y}{2}$

$-4=4+y$

$-4-4=y$

$-8=y$

The value of y is -8.

Therefore the coordinates of endpoint C are (7,-8).