Question

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

Answer 1

`\boxed{\boxed{\pink{\bf \leadsto The \ co-ordinate\ of \ B \ is \ ( -1, -8) }}}`

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 :-

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

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

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

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

`\implies \bf (y-6)/(2) = -7 \\\\\bf\implies y-6=-14 \\\\\bf\implies y = 6 - 14 \\\\\boxed{\red{\bf\implies y = -8}}`

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

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