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The midpoint of overline AB is M(-4, -7). If the coordinates of A are (−7,−6), what are the coordinates of B?

Sagot :

Answer:

[tex]\boxed{\boxed{\pink{\bf \leadsto The \ co-ordinate\ of \ B \ is \ ( -1, -8) }}}[/tex]

Step-by-step explanation:

Given that, The midpoint of overline AB is M(-4, -7). If the coordinates of A are (−7,−6). And we need to find the coordinates of B. We know Midpoint formula is :-

[tex]\large\boxed{\red{\bf Midpoint = \bigg( \dfrac{x_1+x_2}{2} , \dfrac{y_1+y_2}{2}\bigg) }}[/tex]

Let the co ordinates of B be (x , y ) .

Now , on substituting the respective values ,we have :-

[tex]\bf\implies Midpoint = \bigg( \dfrac{x_1+x_2}{2} , \dfrac{y_1+y_2}{2}\bigg) \\\\\bf \implies (-4,-7) = \bigg( \dfrac{x -7}{2} , \dfrac{y-6}{2}\bigg) \\\\\bf \implies \dfrac{x -7}{2} = (-4) \\\\\bf \implies x - 7 = -8 \\\\\bf\implies x = -8+7 \\\\\boxed{\red{\bf \implies x = (-1) }}[/tex]

[tex]\implies \bf \dfrac{y-6}{2} = -7 \\\\\bf\implies y-6=-14 \\\\\bf\implies y = 6 - 14 \\\\\boxed{\red{\bf\implies y = -8}}[/tex]

Hence the value of x coordinate is (-1) and y - coordinate is (-8) .

Hence the coordinate of B is (-1,-8)

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