Question

M(5, 7) is the midpoint of RS. The coordinates of S are (6, 9). What are the coordinates of R?

Answer 1

Coordinate R is at (4,5)

Answer 2

Answer:

The coordinates of R are $(x_1,y_1)=(4,5)$

Step-by-step explanation:

Given : M(5, 7) is the midpoint of RS. The coordinates of S are (6, 9).

To find : What are the coordinates of R?

Solution :

We have given,

A line RS which has a mid point M.

Let, the coordinates of R be $(x_1,y_1)$

The coordinates of S are $(x_2,y_2)=(6, 9)$

The coordinates of M are  $(x_3,y_3)=(5,7)$

Applying mid-point formula,

$(x_3,y_3)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$(5,7)=(\frac{x_1+6}{2},\frac{y_1+9}{2})$

Solve separately,

x- coordinate is

$\frac{x_1+6}{2}=5$

$x_1+6=10$

$x_1=4$

y- coordinate is

$\frac{y_1+9}{2}=7$

$y_1+9=14$

$y_1=5$

So, The coordinates of R are $(x_1,y_1)=(4,5)$