Question

M(9, 8) is the midpoint of RS . The coordinates of S are (10, 10). What are the coordinates of R?

Answer 1

Answer: D) (8, 6)

Step-by-step explanation:

If (x,y) is a midpoint of a line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ such that

$x=\dfrac{x_1+x_2}{2}$ and $y=\dfrac{y_1+y_2}{2}$  (1)

Given : M(9, 8) is the midpoint of RS . The coordinates of S are (10, 10).

Let The coordinate of point R be (a,b).

Using (1) , we have

$9=\dfrac{a+10}{2}$ and $8=\dfrac{b+10}{2}$  

$\Rightarrow\ 2(9)=a+10$and $2(8)=b+10$  

$\Rightarrow\ 18=a+10$and $16=b+10$  

$\Rightarrow\ a=18-10=8$and $b=16-10=6$  

i.e. (a,b) = (8, 6)

Hence, the coordinates of R = (8, 6)

Thus , the correct answer is D) (8, 6)

Answer 2

Answer:

D) (8, 6)

Step-by-step explanation:

Given: M(9, 8) is the midpoint of RS . The coordinates of S are (10, 10).

Here we have to use the mid-point formula:

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

Here (x, y) is the midpoint.

(x, y) = M(9, 8)

(x2, y2) = (10, 10)

Here x = 9, y = 8 and x2 = 10 and y2 = 10

Now let's plug in these values in the mid-point formula and find (x1, y1)

$9 = \frac{x_1 + 10}{2} ; 8 = \frac{y_1 + 10}{2}$

Let's simplify and find the value of x1 and y1

$18 = x_1 + 10 ; 16 = y_1 + 10$

$x_1 = 18 -10 ; y_1 = 16 -10$

$x_1 = 8 ; y_1 = 6$

So the coordinates of R(8, 6)