Question

Find the missing endpoint if S is the midpoint RT

S(-4,-6) and T (-7,-3) Find R

Answer 1

Answer:  R = (-1, -9)

Step-by-step explanation:

Use the midpoint formula (sum of the endpoints divided by 2 equals the midpoint). Separate the x's and y's to solve more easily.

$\dfrac{x_t+x_r}{2}=x_s\qquad \qquad \qquad \dfrac{y_t+y_r}{2}=y_s\\\\\\\dfrac{-7+x_r}{2}=-4 \qquad \qquad \qquad \dfrac{-3+y_r}{2}=-6\\\\\\-7+x_r=-8\qquad \qquad \qquad -3+y_r=-12\\\\\\.\qquad x_r=-1\qquad \qquad \qquad \qquad y_r=-9\\\\\\.\qquad \qquad \qquad \lagre\boxed{(x_r, y_r)=(-1, -9)}$

Answer 2

Answer:

R(-1,-9)

Step-by-step explanation:

Given: S(-4,-6) and T(-7,-3)

Let coordinate of R(a,b)

Mid-point: This point is equi-distance from both end of line.

Mid-point formula: $(x,y)=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$

$x\rightarrow \dfrac{x_1+x_2}{2}$

$y\rightarrow \dfrac{y_1+y_2}{2}$

$x_1\rightarrow a$

$y_1\rightarrow b$

$x_2\rightarrow -7$

$y_2\rightarrow -3$

$x\rightarrow -4$

$y\rightarrow -6$

$-4=\dfrac{a-7}{2}$                  $-6=\dfrac{b-3}{2}$

$-8=a-7$                         $-12=b-3$

$a=-1$    and    $b=-9$

Hence, The coordinate of R(-1,-9)