In the standard (x,y) coordinate plane, point M with coordinates (5,4) is the midpoint of AB, and B has coordinates (7,3). What are the coordinates of A ?

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In the standard (x,y) coordinate plane, point M with coordinates (5,4) is the midpoint of AB, and B has coordinates (7,3). What are the coordinates of A ?

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Answer 1 · 2016-07-27T04:26:38

Coordinates of A are $(3, 5)$ $(3,5)$

Explanation:

In a segment if $A (x_{1}, y_{1})$ $A(x_1,y_1)$ and $B (x_{2}, y_{2})$ $B(x_2,y_2)$ are coordinates of its end points, the coordinates of midpoint $M$ $M$ are $\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}$ $(x_1+x_2)/2,(y_1+y_2)/2$ .

Now we are given $A (x_{1}, y_{1})$ $A(x_1,y_1)$ and $B (7, 3)$ $B(7,3)$ , hence midpoint is $\frac{x_{1} + 7}{2}, \frac{y_{1} + 3}{2}$ $(x_1+7)/2,(y_1+3)/2$ , but midpoint is given to be $(5, 4)$ $(5,4)$ .

Hence $\frac{x_{1} + 7}{2} = 5$ $(x_1+7)/2=5$ i.e. $x_{1} + 7 = 5 \times 2 = 10$ $x_1+7=5xx2=10$ and $x_{1} = 10 - 7 = 3$ $x_1=10-7=3$

and $\frac{y_{1} + 3}{2} = 4$ $(y_1+3)/2=4$ i.e. $y_{1} + 3 = 4 \times 2 = 8$ $y_1+3=4xx2=8$ and $x_{1} = 8 - 3 = 5$ $x_1=8-3=5$

Hence, coordinates of A are $(3, 5)$ $(3,5)$

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In the standard (x,y) coordinate plane, point M with coordinates (5,4) is the midpoint of AB, and B has coordinates (7,3). What are the coordinates of A ?

1 Answer

Explanation:

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