Question

Find the missing endpoint if S is the midpoint RT

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

Answer 1

R(-1,-9)

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)=((x_1+x_2)/(2),(y_1+y_2)/(2))`

`x\rightarrow (x_1+x_2)/(2)`

`y\rightarrow (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=(a-7)/(2)`
`-6=(b-3)/(2)`

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

`a=-1` and
`b=-9`

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

Answer 2

Answer: R = (-1, -9)

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.

`(x_t+x_r)/(2)=x_s\qquad \qquad \qquad (y_t+y_r)/(2)=y_s\\\\\\(-7+x_r)/(2)=-4 \qquad \qquad \qquad (-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)}`