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

Answer:

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

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 :-

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

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

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

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

$\implies \bf \dfrac{y-6}{2} = -7 \\\\\bf\implies y-6=-14 \\\\\bf\implies y = 6 - 14 \\\\\boxed{\red{\bf\implies y = -8}}$

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

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

Answer 2

Answer:

let the point of B be x,y

so, (-7+x/2,-6+y/2)=(-4,-7)

now

$\frac{ - 7 + x}{2} = - 4 \\ - 7 + x = - 4 \times 2 \\ x - 7 = - 8 \\ x = - 8 + 7 \\ x = - 1$

$\frac{ - 6 + y}{2} = - 7 \\ y - 6 = - 7 \times 2 \\ y - 6 = - 14 \\ y = - 14 + 6 \\ y = - 8$

B is (-1,-8)