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Nezavi [6.7K]
4 years ago
6

Midpoint (23,- 10), endpoint (15.-16) The other endpoint is

Mathematics
1 answer:
swat324 years ago
3 0

The other endpoint is (31, -4)

<em><u>Solution:</u></em>

Given that midpoint (23,- 10), endpoint (15.-16)

To find: The other endpoint

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

\text {For two points }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right), \text { the midpoint }(x, y) \text { 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) = (23, -10)

(x_1, y_1) = (15, -16)

(x_2, y_2) = ?

<em><u>Substituting the values in formula we get,</u></em>

(23,-10)=\left(\frac{15+x_{2}}{2}, \frac{-16+y_{2}}{2}\right)

On comparing both sides we get,

23=\frac{15+x_{2}}{2} \text { and }-10=\frac{-16+y_{2}}{2}

\begin{array}{l}{46=15+x_{2} \text { and }-20=-16+y_{2}} \\\\ {x_{2}=46-15 \text { and } y_{2}=-20+16} \\\\ {x_{2}=31 \text { and } y_{2}=-4}\end{array}

Thus the other endpoint is (31, - 4)

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\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}

Let's solve ~

\qquad \sf  \dashrightarrow \: 2m - 3 - 5 =  - m + 10

\qquad \sf  \dashrightarrow \: 2m + m = 10 + 3 + 5

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