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mars1129 [50]
3 years ago
13

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 endp

oint S.
Mathematics
1 answer:
Oksanka [162]3 years ago
8 0

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

<h3><u>Solution:</u></h3>

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

<em><u>The formula for midpoint is given as:</u></em>

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

m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{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(\frac{23+x_{2}}{2}, \frac{14+y_{2}}{2}\right)

Comparing both the sides we get,

\begin{aligned}&13=\frac{23+x_{2}}{2} \text { and } 8=\frac{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)

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