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evablogger [386]
3 years ago
6

The midpoint of AB is M(-5,1). If the coordinates of A are (-4,-5), what are the coordinates of B?

Mathematics
1 answer:
Elenna [48]3 years ago
5 0

<u>ANSWER:</u>

The midpoint of AB is M(-5,1). The coordinates of B are (-6, 7)

<u>SOLUTION: </u>

Given, the midpoint of AB is M(-5,1).  

The coordinates of A are (-4,-5),  

We need to find the coordinates of B.

We know that, mid-point formula for two points A(x_{1}, y_{1}) and B (x_{1}, y_{2}) is given by

M\left(x_{3}, y_{3}\right)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)

Here, in our problem, \mathrm{x}_{3}=-5, \mathrm{y}_{3}=1, \mathrm{x}_{1}=-4 \text { and } \mathrm{y}_{1}=-5

Now, on substituting values in midpoint formula, we get

(-5,1)=\left(\frac{-4+x_{2}}{2}, \frac{-5+y_{2}}{2}\right)

On comparing, with the formula,

\frac{-4+x_{2}}{2}=-5 \text { and } \frac{-5+y_{2}}{2}=1

-4+\mathrm{x}_{2}=-10 \text { and }-5+\mathrm{y}_{2}=2

\mathrm{x}_{2}=-6 \text { and } \mathrm{y}_{2}=7

Hence, the coordinates of b are (-6, 7).

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