Mathematics: M(5, 7) is the midpoint of rs. the coordinates of s are (6, 9). what are the coordinates of r?

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M(5, 7) is the midpoint of rs. the coordinates of

Isabella1319

05.01.2022

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)

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