Question

The midpoint of RS¯¯¯¯¯¯¯ is M. Use the given endpoint R(23, 14) and midpoint M(13, 8) to find the coordinates of the other endpoint S.

Answer 1

The coordinates of other endpoint S is (3, 2)

Solution:

Given that midpoint of RS is M

Given endpoint R(23, 14) and midpoint M(13, 8)

To find: coordinates of the other endpoint S

The formula for midpoint is given as:

For a line containing containing two points
`(x_1, y_1)` and
`(x_2, y_2)` midpoint is given as:

`m(x, y)=\left((x_(1)+x_(2))/(2), (y_(1)+y_(2))/(2)\right)`

Here in this problem,

m(x, y) = (13, 8)

`(x_1, y_1) = (23, 14)\\\\(x_2, y_2) = ?`

Substituting the given values in above formula, we get

`(13,8)=\left((23+x_(2))/(2), (14+y_(2))/(2)\right)`

Comparing both the sides we get,

`\begin{aligned}&13=(23+x_(2))/(2) \text { and } 8=(14+y_(2))/(2)\\\\&26=23+x_(2) \text { and } 16=14+y_(2)\\\\&x_(2)=3 \text { and } y_(2)=2\end{aligned}`

Thus the coordinates of other endpoint S is (3, 2)